Determine The Equation Of A Quadratic Function Worksheet With Answer Key

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Determine the Equation of a Quadratic Function
Equations of quadratics can be expressed in standard form, vertex form and factored form. When finding the equation
of a quadratic choose whichever form is easiest to work with. For example, if you are given the vertex of the parabola
then use vertex form.
Three points are necessary to determine the equation of a quadratic function. However, if one of the points is the
vertex, then only 2 points are necessary.
Example : Find the equation of a quadratic function with a vertex at (-2, 5) that passes through the point (4, -8)
Start by writing the general formula for a quadratic function in vertex form:
Sub the vertex into this equation:
Sub in the other point and solve for ‘a’:
Example 2: Find the equation of a quadratic function with x-intercepts at
and passing through the point (-4, 5).
Realize what the other x-intercept must be.
Write the general equation for a quadratic in factored form:
Substitute the x-intercepts into this equation:
Substitute in the other point and solve for ‘a’:
Simplify your final equation (if you have not already). Why should your answer in this case be in standard form?

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