Creating and Graphing Equations Using the x-interceptsAdapted from Walch Education 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-intercepts 2 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-intercepts 3 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-intercepts 4 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-intercepts 5 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-intercepts 6 Substitute –3.5 for x. f(–3.5) = (1.5)(–1.5) Sketch the function based on the zeros and the vertex. 5.3.2: Creating and Graphing Equations Using the x-intercepts 7 FlightCrank, @ www.emusic.com. Download, play, burn MP3s @ www.emusic.com. What You Need, track 04 0 Other 399.5218 - www.emusic.com/albums/28415/ x = –10 –8 –6 –4 –2 0 2 4 6 8 10