Mark M. answered • 12/18/19

Mathematics Teacher - NCLB Highly Qualified

f(x) = a(x - h)^{2} + k

f(x) = a(x + 4)^{2} - 5 insert the vertex

-9 = a(-6 + 4)^{2} - 5 insert point

-4 = a(-2)^{2}

-4 = 4a

-1 = a

f(x) = -(x + 4)^{2} - 5

Esmeralda M.

asked • 12/18/19This is a question in my math study guide, and the teacher won't explain it.

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Mark M. answered • 12/18/19

Mathematics Teacher - NCLB Highly Qualified

f(x) = a(x - h)^{2} + k

f(x) = a(x + 4)^{2} - 5 insert the vertex

-9 = a(-6 + 4)^{2} - 5 insert point

-4 = a(-2)^{2}

-4 = 4a

-1 = a

f(x) = -(x + 4)^{2} - 5

Kerri P. answered • 12/18/19

Certified Mathematics Teacher Grades 7-12

Start with vertex form for a parabola: y = a(x - h)^{2 }+ k. The vertex (-4, -5) can be plugged in as (h, k) so that we have y = a(x + 4)^{2} - 5. We don't know what a is, but if we plug in the other point we were given (-6, -9) as x and y, we will be able to solve for a:

-9 = a(-6 + 4)^{2} - 5

-9 = 4a - 5

a = -1

Now we can plug h, k, and a into the vertex form: **y = -(x + 4)**^{2}** - 5** is the answer!

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