Question

Suppose a parabola has vertex (5,-3) and also passes through the point (6, 1). Write the equation of the parabola in vertex form.

Answer 1

General form for vertex form is:

y = a(x - h)² + k

Where the vertex is the point (h, k). We know this to be (5, -3), so we can substitute the values for h and k to get:

y = a(x - 5)² - 3

We then also have another point (6, 1) that gives us an x and y. Substitute those in to leave one unknown which we can solve for:

1 = a(6 - 5)² - 3

1 = a(1)² - 3

1 = a(1) - 3

1 = a - 3

4 = a

So the equation of this parabola in vertex form is:

y = 4(x - 5)² - 3

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