Question

The parabola grows through left parenthesis negative 8.5 comma negative 3 right parenthesis, peaks at left parenthesis negative 4 comma 2 right parenthesis, then drops to left parenthesis negative 0.5 comma negative 4 right parenthesis. All values are approximate.


Which response is the correct way to write the equation in vertex form for the function?

(1 point)
Responses

y=−14(x+4)2+2
y equals negative Start Fraction 1 over 4 End Fraction left parenthesis x plus 4 right parenthesis squared plus 2

y=−14(x+2)2+4
y equals negative Start Fraction 1 over 4 End Fraction left parenthesis x plus 2 right parenthesis squared plus 4

y=−14(x−2)2+4
y equals negative Start Fraction 1 over 4 End Fraction left parenthesis x minus 2 right parenthesis squared plus 4

y=−14(x−4)2+2
y equals negative Start Fraction 1 over 4 End Fraction left parenthesis x minus 4 right parenthesis squared plus 2

Answer 1

Vertex is (−4, 2) so start with y = a(x + 4)^2 + 2. Using the point (−8.5, −3) gives a ≈ (−3 − 2)/(−8.5 + 4)^2 = −5/20.25 ≈ −1/4.

So the correct choice is y = −1/4 (x + 4)^2 + 2.