Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 10 to 2 and its y-axis ranges from negative 4 to 4, both by 1-unit increments. A concave down parabola is drawn passing through the 2nd, 3rd, and 4th quadrants.
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 minus 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+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 minus 2 right parenthesis squared plus 4

Answer 1

Vertex is (−4, 2) so y = a(x+4)^2 + 2. Use point (−8.5, −3): (−8.5+4)^2 = (−4.5)^2 = 20.25, so −3 = a(20.25)+2 ⇒ a = −5/20.25 = −1/4.

Answer: y = −(1/4)(x+4)^2 + 2.