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
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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
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Identify the x-intercepts and plot the points.
The x-intercepts of the quadratic are the zeros or solutions of the quadratic.
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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.
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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.
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Substitute –3.5 for x.
f(–3.5) = (1.5)(–1.5)
Sketch the function based on the zeros and the vertex.
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