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

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Presentation transcript:

Creating and Graphing Equations Using the x - intercepts Adapted 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-intercepts2

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 : Creating and Graphing Equations Using the x-intercepts3

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

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 = – : Creating and Graphing Equations Using the x-intercepts5

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 – : Creating and Graphing Equations Using the x-intercepts6 f(x) = (x + 5)(x + 2) Original equation f(–3.5) = (– )(– ) Substitute –3.5 for x. f(–3.5) = (1.5)(–1.5)Simplify. f(–3.5) = –2.25

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

THANKS FOR WATCHING! Ms. Dambreville