Question

question 11 (1 point)
write an equation of the parabola in intercept form.
x-intercepts of 2 and -8; passes through (-6, -4)
a ( y = -\frac{1}{4}(x + 2)(x - 8) )
b ( y = 4(x - 2)(x + 8) )
c ( y = -4(x + 2)(x - 8) )
d ( y = \frac{1}{4}(x - 2)(x + 8) )
question 12 (1 point)
which equation has a graph that is a line passing through the point (-1,

Explanation:

Step1: Recall intercept form

The intercept form of a parabola is \( y = a(x - p)(x - q) \), where \( p \) and \( q \) are the x - intercepts. Given x - intercepts are 2 and - 8, so \( p = 2 \) and \( q=-8 \). Then the equation becomes \( y=a(x - 2)(x + 8) \).

Step2: Substitute the point \((-6,-4)\)

We substitute \( x=-6 \) and \( y = - 4 \) into the equation \( y=a(x - 2)(x + 8) \).

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Step3: Solve for \( a \)

Divide both sides of the equation \( - 4=-16a \) by - 16: \( a=\frac{-4}{-16}=\frac{1}{4} \).

Step4: Write the equation

Substitute \( a = \frac{1}{4} \) back into the intercept form equation \( y=a(x - 2)(x + 8) \). We get \( y=\frac{1}{4}(x - 2)(x + 8) \).

Answer:

d. \( y=\frac{1}{4}(x - 2)(x + 8) \)