Question

The polynomial function F(x) = 2x2 +8x-7 has a critical point at which of the
following x-values?
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A. x=-7
B. x= -2
C. x= 0
D. x = 2

Answer 1

Answer:

Option B $x=-2$

Step-by-step explanation:

we know that

The critical point of a function are the points on the graph of a function where the derivative is zero or the derivative does not exist.

we have

$f(x)=2x^{2}+8x-7$

step 1

Take the derivative of the function

$f'(x)=4x+8$

step 2

Set that derivative equal to 0 and solve for x. Each x value you find is known as a critical number

$f'(x)=0$

$4x+8=0$

$4x=-8$

$x=-2$

Alternative Method

The critical point of the quadratic equation is the vertex, because the function changes from decreasing to increasing at that point (In this problem the vertex is a minimum)

we have

$f(x)=2x^{2}+8x-7$

Convert into vertex form

$f(x)+7=2x^{2}+8x$

$f(x)+7=2(x^{2}+4x)$

$f(x)+7+8=2(x^{2}+4x+4)$

$f(x)+15=2(x^{2}+4x+4)$

$f(x)+15=2(x+2)^{2}$

$f(x)=2(x+2)^{2}-15$

the vertex is the point (-2,-15)

therefore

The x-coordinate of the critical point is x=-2