Quadratic equations (Minimum value, turning point)
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How to find the minimum and maximum value of a quadratic equation How to find the Y-intercept of a quadratic graph and equation How to calculate the equation of the line of symmetry of a quadratic curve How to find the turning point (vertex) of a quadratic curve, equation or graph.
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Similar to Quadratic equations (Minimum value, turning point)
02.21.2020 Algebra I Quadraic Functions.ppt
The document provides an agenda and lesson plan for an Algebra I class that includes the following:
1. The class will begin with a D.E.A.R activity called "Jaguar Ascensions" followed by taking Cornell notes on the lesson.
2. Students will then summarize their notes and have a teacher dialogue.
3. A number sense routine involving finding a missing number in an equation will be completed.
4. The remainder of the class will cover topics on quadratic functions including graphing quadratic functions in standard, vertex, and intercept forms as well as solving quadratic equations through factoring and using the quadratic formula.
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The document discusses how to graph quadratic equations in the form of y = ax^2 + bx + c. It states that the graphs are parabolas with a vertex and center line. To graph a parabola, one finds the vertex, another point such as the y-intercept, reflects that point across the center line, and finds the x-intercept to complete the parabola.
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The document discusses graphing quadratic functions in standard form (y=ax^2 + bx + c). It explains that the graph is a parabola that can open up or down depending on whether a is positive or negative. The line of symmetry for the parabola passes through the vertex and is given by the equation x=-b/2a. The steps to graph are: 1) find the line of symmetry, 2) plug the x-value into the original equation to find the vertex, 3) find two other points and reflect them across the line of symmetry.
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The document discusses three forms of quadratic equations - standard form, vertex form, and intercept form. It provides the key characteristics of each form and steps for graphing equations written in each form. Standard form is easiest to solve by factoring. Vertex form shows the vertex and axis of symmetry. Intercept form directly lists the x-intercepts. Converting between forms involves multiplying out terms.
6. 1 graphing quadratics
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Quadratic equations
This document discusses quadratic equations and methods for solving them. It begins by defining quadratic equations as second degree polynomial equations of the form ax^2 + bx + c = 0, where a is not equal to 0. It then presents several methods for finding the roots or solutions of quadratic equations: factoring, completing the square, and using the quadratic formula. Examples are provided to illustrate each method. The document also discusses graphing quadratic functions and key features of parabolas such as vertex, axis of symmetry, and direction of opening.
G9_Q2_W2_L2_GraphsofQUadraticFunction.pdf
The document discusses key concepts about quadratic functions including:
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2) The axis of symmetry of a parabola passes through the vertex (highest/lowest point) and can be found using the equation x = -b/2a.
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The document discusses how to graph quadratic functions of the form y = ax^2 + bx + c. It explains that the graph is a parabola that may open up or down. It describes how to find the line of symmetry, which is -b/2a, and how this line passes through the vertex. It provides steps to find the vertex by plugging the x-value from the line of symmetry into the original equation. Finally, it demonstrates graphing a parabola by finding two additional points and reflecting them across the line of symmetry.
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This document provides information about various geometric concepts in Cartesian coordinates (R2). It defines R2 as the set of all ordered pairs (a,b) of real numbers. It discusses representing points in R2 using coordinates, and defines concepts like distance, midpoint, linear equations, circles, parabolas, ellipses, and hyperbolas. It provides examples of finding distances between points, finding midpoints of line segments, graphing linear equations, finding equations of circles, and identifying graphs of parabolas, ellipses and hyperbolas based on their standard equations.
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Math project
The document discusses key concepts about linear equations in two variables including:
1) It describes the Cartesian coordinate plane and how to plot points based on their x and y coordinates.
2) It explains how to find the slope, y-intercept, and x-intercept of a linear equation graphically and algebraically.
3) It provides examples of rewriting linear equations in slope-intercept form (y=mx+b) and using intercepts and slopes to graph lines on the coordinate plane.
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This document provides information about graphing quadratic functions. It defines the standard form of a quadratic function as y = ax^2 + bx + c and explains that the sign of a determines if the parabola opens up or down. It describes how to find the axis of symmetry, vertex, domain and range. The steps to graph a quadratic function are given as finding the axis of symmetry, the vertex, and then two other points to reflect across the axis and connect with a smooth curve. Methods for finding the axis of symmetry, vertex, y-intercept and solutions are demonstrated through examples.
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This document discusses key concepts related to graphing linear and quadratic equations:
- It explains how to graph linear equations in the form of y=mx+c by plotting points based on the slope (m) and y-intercept (c).
- It shows how to find the equation of a line given two points on the line by calculating the slope.
- It describes how the shape of a quadratic graph (y=ax2+bx+c) depends on the values of a, b, and c, and how to find the vertex of a parabola.
- It demonstrates several methods to determine the equation of a quadratic function given points or the vertex.
Coordinate geometry
This document provides information on various concepts in elementary and additional mathematics including:
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- Equations of lines
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- Intersecting lines and finding intersection points
- Perpendicular bisectors
- Finding the area of polygons
It includes examples of applying these concepts to solve problems involving lines, midpoints, gradients, intersections, perpendiculars, and calculating areas.
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
The document discusses linear equations and graphing linear relationships. It defines key terms like slope, y-intercept, x-intercept, and provides examples of writing linear equations in slope-intercept form and point-slope form given certain information like a point and slope. It also discusses using tables and graphs to plot linear equations and find slopes from graphs or between two points. Real-world examples of linear relationships are provided as well.
Graphing A Parabola
The document discusses how to graph a parabola by finding its axis of symmetry and turning point. The axis of symmetry is the line that cuts the parabola into two equal halves and passes through the turning point. To find the axis of symmetry, use the formula x=-b/2a where a and b are the coefficients of the quadratic equation. The turning point is found by substituting the axis of symmetry back into the original equation and is written as an ordered pair (x, y). An example parabola y=x^2+6x-2 is used to demonstrate finding its axis at x=3 and turning point of (3, 25).
Equation Of A Line
This document discusses different methods for finding the equation of a line, including:
1) Given the slope and y-intercept
2) Using a graph
3) Given a point and the slope
4) Given two points
It provides examples of how to write the line equation using each method.
chapter1_part2.pdf
1. This document discusses linear equations, slope, graphing lines, writing equations in slope-intercept form, and solving systems of linear equations.
2. Key concepts explained include slope as rise over run, the different forms of writing a linear equation, finding the x- and y-intercepts, and using two points to write the equation of a line in slope-intercept form.
3. Examples are provided to demonstrate how to graph lines based on their equations in different forms, find intercepts, write equations from two points, and solve systems of linear equations.
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Quadratic equations (Minimum value, turning point)
- 2. The vertex is the point of the curve, where the line of symmetry crosses. On the graph, the vertex is shown by the arrow. The co-ordinates of this vertex is (1,-3) The vertex is also called the turning point. HOW TO FIND THE VERTEX
- 3. To find the Y-intercept, you look and the C coefficient of the quadratic equation. For example, if the quadratic equation is 5x2 + 3x -2, the Y- intercept here is -2 because this is the C coefficient in the quadratic equation. HOW TO CALCULATE THE Y-INTERCEPT C value
- 4. Every parabola has an axis of symmetry. This line passes through the vertex and divides the parabola into two halves that are mirror images. To find the Line of Symmetry of a quadratic equation (parabola), you use the formula; x= -b/2a For example; Find the line of symmetry (or axis of symmetry) for y = x2 – x -9 Find the coefficients of A and B and plug them into the formula A=1, B=-1 X= -b/2a X= -(-1)/2(1) X=1/2 X=0.5 The answer must include x= (so answer is x=0.5) HOW TO CALCULATE THE LINE OF SYMMETRY
- 5. Question: Find the minimum value of y= x2 +6x +10 To find the minimum value, first identify the A and B coefficients. (A=1, B=6). Use the equation X=-b/2a and plug in the coefficients of A and B. X=-(6)/2(1) X=-6/2 X=-3 Then plug the answer (the X value) into the original parabola to find the minimum value. X2 + 6x + 10 (-3)2 + 6(-3) + 10 9-18+10=1 HOW TO CALCULATE THE MINIMUM VALUE
- 6. Question: Find the vertex (turning point) of y= 3x2 + 12x – 12 First identify the coefficients of A and B (A=3, B=12) and plug them into this equation; x=-b/2a X=-(12)/2(3) X=-12/6 X=-2 so this is the x-coordinate of the vertex Then plug that value of X into the original parabola: 3(-2)2 + 12(-2) – 12 12 – 24 – 12 = -24 this is the y-coordinate of the vertex So the vertex (turning point of this parabola is (-2,-24) HOW TO CALCULATE THE VERTEX (TURNING POINT)