The document discusses three forms of quadratic equations - standard form, vertex form, and intercept form. It provides the definitions and formulas for each form. It then explains how to graph each form by identifying key features of the equation, finding important points like the vertex, axis of symmetry, intercepts, and connecting points to sketch the parabolic curve. Graphing techniques include using the value of a to determine the opening direction, using b and c for standard form, using h and k for vertex form, and using p and q for intercepts form.

1. Quadratics! Three Forms and Graphing

2. Standard Form Standard Form is y=ax ²+bx+c where a does not equal 0 Tricks for Factoring in this Form: If a and c are both perfect squares, try one of the special patterns: Difference of two squares: a²-b²=(a+b)(a-b) Ex. x²-4=(x+2)(x-2) Because the square root of x² is x and the square root of 4 is 2 Perfect Square Trinomial: Use if a=1 and b is a perfect square Ex. x²+6x+9=(x+3)² because the square root of x² is x, the square root of 9 is 3, and 3+3=6, which is the b term Before factoring, check to see if the terms have a Greatest Common Factor

3. Vertex Form Vertex Form: y=(x-h) ²+k In order to factor from vertex form, it must be converted to standard form

4. Intercept Form Intercept Form: y=a(x-p)(x-q) Just like vertex form, you must convert intercept form to vertex form in order to factor it

5. Graphing in Standard Form Tricks from the Equation: a will tell you if the graph opens up or down, which affects whether there is a minimum or a maximum If a is positive, the graph opens up, if a is negative, the graph opens down c will tell you the y-intercept of the graph Steps for Graphing: Find the vertex: (-b/2a, f(-b/2a)) To find the y-coordinate of the vertex, plug the x back into the equation and solve To find two more points, use info you already know: You know that c is where the graph crosses the y-axis, so use that as one point To find the other point, you need to know the axis of symmetry. It’s simple to find the axis of symmetry; it’s simply a line running parallel to the y-axis that goes through the vertex. (You just need to know the x-coordinate of the vertex) Once you have the line drawn, simply mark a point an equal distance from the line of symmetry that is equal to the distance from the y-intercept to the line of symmetry Connect all of these points with a smooth line and label

6. Graphing in Vertex Form Tricks from the Equation: a is has the same rules as a in standard form The vertex is (h,k) h determines how far left or right the parabola is k determines how far up or down the parabola is Steps for Graphing: Determine and plot the vertex (h,k) Draw the axis of symmety. The equation for this is x=h Find coordinates of a point to the left and right of the vertex (A good trick is to go over left or right by one unit and up by the value of a (or go down if a is negative) however, this trick only works once) Connect the points and label

7. Graphing in Intercept Form Tricks from the equation: p and q are the x-intercepts of the parabola a is still the same as compared to standard and vertex form The y-intercept is apq Steps for Graphing: Plot the x-intercepts Find the coordinates of the vertex. Vertex=(p+q/2, f(p+q/2)) Plot the vertex and the axis of symmetry (axis of symmetry equation is x=p+q/2) Connect the points and label

8. Now go watch the videos that demonstrate graphing!