Write an equation for a quadratic function that has a vertex of(-1,4) and the parabola opens down

Answer 1

y = a(x - h)² + k, where (h,k) is the vertex. The parabola opens downward only when a < 0.

So, for example, the graph of y = -2(x + 1)² + 4 satisfies the given conditions.

Answer 2

There are three ways to write this equation: 1) Vertex form, 2) Standard form, 3) Factored form.

Given the vertex and the opening direction, it's easiest to do this in vertex form.

To start, the vertex form is y=a(x-h)² +k

where (h,k) is the vertex, and a determines opening behavior. Since we are opening down, a must be negative.

Therefore, y=-1(x+1)²+4 is an acceptable answer.

Answer 3

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1. The vertex form for a quadratic equation is --> y=a(x-h)^2+k
2. (h,k) is the vertex of the parabola
3. "opens downward" --> Coefficient of (x-h)^2 has to be negative (a has to be negative)
4. (h,k) --> (-1,4)
5. An equation that suits the given requirements may be --> y=-1(x+1)^2+4

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Answer 4

See the videa.