Math  /  Algebra

Question7. Jonsider the function P(x)=2x28x7P(x)=-2 x^{2}-8 x-7 7a7 a Find the xx-coordinate of the vertex x=x=
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Studdy Solution

STEP 1

1. The function P(x)=2x28x7 P(x) = -2x^2 - 8x - 7 is a quadratic function.
2. The vertex form of a quadratic function is useful for finding the vertex.
3. The formula for the x x -coordinate of the vertex of a quadratic function ax2+bx+c ax^2 + bx + c is x=b2a x = -\frac{b}{2a} .

STEP 2

1. Identify the coefficients a a and b b from the quadratic function.
2. Use the vertex formula to calculate the x x -coordinate of the vertex.

STEP 3

Identify the coefficients a a and b b in the quadratic function P(x)=2x28x7 P(x) = -2x^2 - 8x - 7 .
Here, a=2 a = -2 and b=8 b = -8 .

STEP 4

Apply the vertex formula x=b2a x = -\frac{b}{2a} to find the x x -coordinate of the vertex.
Substitute a=2 a = -2 and b=8 b = -8 into the formula:
x=82(2) x = -\frac{-8}{2(-2)}

STEP 5

Simplify the expression:
x=84 x = -\frac{-8}{-4} x=84 x = \frac{8}{4} x=2 x = 2
The x x -coordinate of the vertex is:
2 \boxed{2}

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