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nika2105 [10]
3 years ago
8

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

Mathematics
2 answers:
Inessa05 [86]3 years ago
4 0

Answer:

The vertex is at (1, -108).

Step-by-step explanation:

We have the function:

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

And we want to find its vertex point.

Note that this is in factored form. Hence, our roots/zeros are <em>x</em> = 7 and <em>x</em> = -5.

Since a parabola is symmetric along its vertex, the <em>x-</em>coordinate of the vertex is halfway between the two zeros. Hence:

\displaystyle x=\frac{7+(-5)}{2}=\frac{2}{2}=1

To find the <em>y-</em>coordinate, substitute this back into the function. Hence:

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

Therefore, our vertex is at (1, -108).

Ierofanga [76]3 years ago
4 0

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

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