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A quadratic function has roots at 2 and 4 and a vertex at (3, −2). What is the equation of the function in vertex form?

User Enkum
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Final answer:

The equation of a quadratic function with roots at 2 and 4 and a vertex at (3, -2) is y = 2(x - 3)^2 - 2.

Step-by-step explanation:

To find the equation of the quadratic function in vertex form when given the roots at 2 and 4 and the vertex at (3, -2), we follow a step-by-step process. The vertex form of a quadratic is given by:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola. Given the vertex (3, -2), we have:

y = a(x - 3)^2 - 2

Since the roots are 2 and 4, the quadratic function will be zero at these points. Substituting x = 2:

0 = a(2 - 3)^2 - 2

0 = a(1)^2 - 2

a = 2

Now substituting x = 4:

0 = a(4 - 3)^2 - 2

0 = a(1)^2 - 2

Again, a = 2

So, the equation of the quadratic function in vertex form is:

y = 2(x - 3)^2 - 2

User Khaled Al Hourani
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4 votes

Answer:

Step-by-step explanation:

User TunaMaxx
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