2. Creating and Graphing Equations Using the x - intercepts Adapted from Walch Education

3. Intercept Form A quadratic function in standard form can be created from the intercept form. The intercept form of a quadratic function is f(x) = a(x – p)(x – q), where p and q are the zeros of the function. The x-intercepts, also known as the zeros, roots, or solutions of the quadratic, are often identified as p and q. The axis of symmetry is located halfway between the zeros. To determine its equation, use the formula 5.3.2: Creating and Graphing Equations Using the x-intercepts2

4. Practice Identify the x-intercepts, the axis of symmetry, and the vertex of the quadratic f(x) = (x + 5)(x + 2). Use this information to graph the function. 5.3.2: Creating and Graphing Equations Using the x-intercepts3

5. Identify the x -intercepts and plot the points. The x-intercepts of the quadratic are the zeros or solutions of the quadratic. 5.3.2: Creating and Graphing Equations Using the x-intercepts4

6. Determine the axis of symmetry to find the vertex. The axis of symmetry is the line that divides the parabola in half. Insert the values of x into the formula to find the midpoint. Let p = –5 and q = –2. The equation of the axis of symmetry is x = –3.5. 5.3.2: Creating and Graphing Equations Using the x-intercepts5

7. Y-value of the vertex Substitute –3.5 for x in the original equation to determine the y-value of the vertex. The y-value of the vertex is –2.25. 5.3.2: Creating and Graphing Equations Using the x-intercepts6 f(x) = (x + 5)(x + 2) Original equation f(–3.5) = (–3.5 + 5)(–3.5 + 2) Substitute –3.5 for x. f(–3.5) = (1.5)(–1.5)Simplify. f(–3.5) = –2.25

8. Sketch the function based on the zeros and the vertex. 5.3.2: Creating and Graphing Equations Using the x-intercepts7

9. THANKS FOR WATCHING! Ms. Dambreville