Today: Warm-Up Review Quadratic CharacteristicsGraphing Various Quadratic Functions Class Work
Warm- Up Exercises The slope is 2, which is positive and the Y- intercept is -2 Therefore, the correct graph is A
Warm- Up ExercisesWrite the equation for the line below: The Y-intercept is: 0 The slope is: 2 The equation of the line is: Y = 2x
Warm- Up Exercises3. Write the inequality for the graph below The Y-intercept is: 2 The slope is: -3 The line is solid, not dotted. The equation is: Y < -3x + 2
Quadratic Review A variable in a quadratic equation can have an exponent of 2, but no higher. The following are all examples of quadratic equations:x2 = 25, 4y2 + 2y - 1 = 0, y2 + 6y = 0, x2 + 2x - 4 = 0 The standard form of a quadratic is written as: ax2 + bx + c = 0, where only a cannot = 0 A. The graphs of quadratics are not straight lines, they are always in the shape of a Parabola.
Graphing Parabolas & Parabola Terminology Important points on a Parabola:1.Axis of Symmetry:The axis of symmetry is the verticleor horizontal line which runs through the exact centerof the parabola.
Graphing Parabolas & Parabola TerminologyImportant points on a Parabola:2. Vertex: The vertex is the highest point (themaximum), or the lowest point (the minimum) on aparabola. Notice that the axis of symmetry always runs through the vertex.
Graphing Various Types of Quadratic EquationsRemember, the standard form of a quadratic equation is: ax2 + bx + c = 0Since the solutions or roots to a standard equation arewhere the line crosses the x-axis, the y value is alwayszero. As such, we can substitute y for zero: y = ax2 + bx + cFinally, since the y variable is dependent on the x, or is afunction of x, we can substitute the y for the function ofx, or (f)x: (f)x = ax2 + bx + cRegardless of which form is presented, the problem issolved in the same way.
Graphing Various Types of Quadratic EquationsIn this lesson, you will graph quadratic functions where b = 0.The first step is to make a table. We can use the following xvalues today: Then complete the values for y and graph the parabola. This must be done for each graph completed today.
Class Work:Girls, do odd problems; Guys even. Create tables for each problem. One problem for each graph.
Finding the Axis of Symmetry and Vertex 1. Finding the Axis of Symmetry: The formula is: x = - b/2a Plug in and solve for y = x2 + 12x + 32We get - 12/2; = -6. The center of the parabola crosses the xaxis at -6. Since the axis of symmetry always runs throughthe vertex, the x coordinate for the vertex is -6 also.
Finding the Axis of Symmetry and Vertex y = x2 + 12x + 32There is one more point left to find and that is they-coordinate of the vertex. To find this, plug in thevalue of the x-coordinate back into the equationand find y.y = -62 + 12(-6) + 32. Y = 36 - 72 + 32; y = - 4 The bottom of the parabola is at -1 on the x axis, and- 4 on the y axis.