Question

Finish the steps below to write a quadratic function for the parabola shown. use the vertex form, f(x) = a(x – h)2 k, and substitute in the values for h and k. f(x) = a(x – 5)2 3 use another point and substitute in values for x and f(x). solve for a. 5 = a(6 – 5)2 3 write the function, using the values for h, k, and a. the function is f(x) = (x – )2 .

Answer 1

The vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]

What is the vertex form of parabola?

Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

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

Here, (h, k) is the vertex point.

Substitute the values for h and k in the above vertex form.

$f(x) = a(x -5)^2+ 3$

Use another point and substitute in values for x and f(x). Solve for a.

$5 = a(6 - 5)^2 +3\\5-3=a(1)\\a=2$

Rewrite the function, using the values for h, k, and a. The function is

$f(x) = 2(x -5)^2+ 3$

Hence, the vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]

Learn more about the vertex form of the parabola here;

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