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## Find the vertex of f(x) = 3(x-7)(x+5) Please show your work. ^^ I’ve been having a bit of trouble with this question :( a

Question

Find the vertex of f(x) = 3(x-7)(x+5)

Please show your work.

^^ I’ve been having a bit of trouble with this question 🙁 although it’s simple quadratics is not my strong suit

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Mathematics
7 months
2021-07-23T08:56:06+00:00
2021-07-23T08:56:06+00:00 2 Answers
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## Answers ( )

Answer:vertex (1, -108)

Step-by-step explanation:First find the zeros

f(x) = 3(x-7)(x+5)

0 = 3(x-7)(x+5)

Using the zero product property

x-7 = 0 x+5 = 0

x = 7 x = -5

The x coordinate of the vertex is the average of the zeros

(7+-5)/2 = 2/2 =1

To find the y coordinate, substitute the x coordinate into the equation

y = 3(1-7)(1+5) = 3(-6)(6) = -108

Answer:The vertex is at (1, -108).

Step-by-step explanation:We have the function:

And we want to find its vertex point.

Note that this is in factored form. Hence, our roots/zeros are

x= 7 andx= -5.Since a parabola is symmetric along its vertex, the

x-coordinate of the vertex is halfway between the two zeros. Hence:To find the

y-coordinate, substitute this back into the function. Hence:Therefore, our vertex is at (1, -108).