Question

What is the equation of the graph below? A graph shows a parabola that opens down and crosses the x axis near one and a half and four and a half. (5 points) y = − (x + 2)2 + 2 y = − (x − 3)2 + 2 y = (x − 2)2 + 2 y = (x + 3)2 + 2

Answer 1

y = -(x-3)² +2

Explanation:

The axis of symmetry is halfway between the zeros, so is about ...

(1.5 + 4.5)/2 = 3

This is the x-coordinate of the vertex. The only equation having a vertex with that x-coordinate is the answer shown above.

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The equation of a parabola with vertex (h, k) is ...

y = a(x -h)² +k

If the parabola opens downward and has real roots, the value of "a" will be negative and the value of "k" will be positive.