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Consider the parabola given by the equation: f ( x ) = x 2 + 6 x − 8 Find the following for this parabola: A) The value of f ( − 5 ) : Correct B) The vertex = (Incorrect,Incorrect) C) The y intercept is the point (0,Correct) D) Find the two values of x that make f ( x ) = 0 . Round your answers to two decimal places. Write the values as a list, separated by commas: x = Incorrect

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Let's go through each part of the question:

A) The value of f(-5):

To find the value of f(-5), we substitute x = -5 into the equation f(x) = x^2 + 6x - 8:

f(-5) = (-5)^2 + 6(-5) - 8

f(-5) = 25 - 30 - 8

f(-5) = -13

B) The vertex:

To find the vertex of the parabola, we use the formula: x = -b/(2a), where a and b are the coefficients of the quadratic equation.

For the equation f(x) = x^2 + 6x - 8, a = 1 and b = 6.

Using the formula, we find:

x = -6/(2*1) = -6/2 = -3

To find the corresponding y-coordinate, we substitute x = -3 into the equation:

f(-3) = (-3)^2 + 6(-3) - 8

f(-3) = 9 - 18 - 8

f(-3) = -17

So the vertex is (-3, -17).

C) The y-intercept:

To find the y-intercept, we substitute x = 0 into the equation:

f(0) = (0)^2 + 6(0) - 8

f(0) = 0 - 0 - 8

f(0) = -8

So the y-intercept is (0, -8).

D) Find the values of x that make f(x) = 0:

To find the values of x that make f(x) = 0, we set the equation equal to zero and solve for x:

x^2 + 6x - 8 = 0

Using the quadratic formula or factoring, we find the solutions:

x = (-b ± √(b^2 - 4ac))/(2a)

Plugging in the values a = 1, b = 6, and c = -8, we get:

x = (-6 ± √(6^2 - 4(1)(-8)))/(2(1))

x = (-6 ± √(36 + 32))/2

x = (-6 ± √68)/2

x = (-6 ± 2√17)/2

x = -3 ± √17

So the two values of x that make f(x) = 0 are approximately -3 + √17 and -3 - √17.

User Valerie S
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