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alexdok [17]
3 years ago
11

What is the y value of the vertex of the function f(x)=-(x-3)(x+11)

Mathematics
1 answer:
AnnyKZ [126]3 years ago
4 0

Answer:

49

Step-by-step explanation:

Because there is a minus sign infront of x-3, we can convert x-3 into the negative form:

- * x

- * -3

-x + 3

Which gives us:

(-x + 3)(x + 11)

Now expand the brackets with the formula:

(a + b)(c + d) = ac + ad + bc + bd

-x * x = -x²

-x * 11 = -11x

3 * x = 3x

3 * 11 = 33

-x² - 11x + 3x + 33

-x² - 8x + 33

The formula for finding the x coordinate of a vertex in a quadratic equation is:

x = \frac{-b}{2a}

Plug known variables in:

x = \frac{-(-8)}{2(-1)}

x = \frac{8}{-2}

x = -4

Now, to find the y coordinate, plug this variable back into the quadratic equation:

-x² - 8x + 33

y = -(-4^2) - (32) + 33\\y = -16 + 32 + 33\\\\

y = 49

So the y coordinate of the vertex is 49.

Hope this helps!

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