Question

H(t)=-4t^2+8t+32 vertex form

Answer 1

The given quadratic function h(t) = -4t^2 + 8t + 32 is converted to vertex form by completing the square, resulting in the vertex form h(t) = -4(t - 1)^2 + 36.

Step-by-step explanation:

The student has presented the quadratic function h(t) as -4t^2 + 8t + 32 and seeks to write it in vertex form. To convert a quadratic function to vertex form, we need to complete the square. Here's the step-by-step process for transforming the given quadratic equation into vertex form:

• h(t) = -4t^2 + 8t + 32 (original equation)
• h(t) = -4(t^2 - 2t) + 32 (factor out -4 from the first two terms)
• h(t) = -4(t^2 - 2t + 1 - 1) + 32 (complete the square by adding and subtracting (b/2a)^2, which is 1 in this case)
• h(t) = -4((t - 1)^2 - 1) + 32 (rewrite the squared term and simplify)
• h(t) = -4(t - 1)^2 + 36 (final vertex form by multiplying through the -4 and adding to 32)

The vertex form of the given quadratic function is h(t) = -4(t - 1)^2 + 36.