Question

Use knowledge of reference points to write an equation for the quadratic function that has a vertex at (4,-3) and passes through (6,-1) Must show work, and answer must be in vertex form.

Answer 1

The quadratic equation that has a vertex at (4,-3) and passes through (6,-1)  is given by:

y = 0.5(x - 4)² - 3.

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (4,-3), hence:

h = 4, k = -3.

The equation is:

y = a(x - 4)² - 3.

When x = 6, y = -1, hence we use it to find the leading coefficient a as follows:

-1 = a(6 - 4)² - 3

4a = 2.

a = 0.5.

Hence the equation is:

y = 0.5(x - 4)² - 3.

More can be learned about quadratic equations at brainly.com/question/24737967

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