Question

What is the correct standard form of the equation of the parabola?

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Answer 1

y=1/4(x−2)2−5.

Explanation:

The equation of the parabola with vertex (h,k) is y=a(−h+x)^2+k.

Thus, the equation of the parabola is y=a(x−2)^2−5.

To find a, use the fact that the parabola passes through the point (4,−4): −4=4a−5.

Solving this equation, we get that a= 1/4.

Thus, the equation of the parabola is y=1/4 (x−2)2−5.