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Maurinko [17]
3 years ago
7

Can anybody help me out on this? Thanks.

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
8 0

Answer:

x = 3

Step-by-step explanation:

Given

y = -2x^2 + 12x +7

Required

The x coordinate of the vertex

Using the general form:

y = ax^2 +bx +c

The x coordinate is:

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

In y = -2x^2 + 12x +7

a = -2

b = 12

c = 7

So, we have:

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

x = -\frac{12}{2*-2}

x = -\frac{12}{-4}

x = \frac{12}{4}

x = 3

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=================================

Work Shown:

(g°h)(x) is the same as g(h(x))

So, (g°h)(0) = g(h(0))

Effectively h(x) is the input to g(x). Let's first find h(0)

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Now let's find g(3)

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alternatively, you can plug h(x) algebraically into the g(x) function

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g( h(x) ) = -3*( h(x) ) ... replace all x terms with h(x)

g( h(x) ) = -3*(x^2 + 3) ... replace h(x) on right side with x^2+3

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Next we can plug in x = 0

g( h(0) )  = -3(0)^2 - 9

g( h(0) ) = -9

we get the same result.

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