Question

Write the quadratic function in vertex form. y = x2 + 8x + 18

Answer 1

Subtract 18 from both sides:
y - 18 = x^2 + 8x

Complete the square by adding 16 to both sides:
y - 18 + 16 = x^2 + 8x + 16
y - 2 = x^2 + 8x + 16

Express x^2 + 8x + 16 in binomial square form:
y - 2 = (x + 4)^2

Add 2 to both sides:
y = (x + 4)^2 + 2

Answer 2

Remember, the vertex form is

y = a(x - h)^2 + k

In this case a = 1, h = -4, k = 2

Answer 3

Thanks! Could you help me out with this problem? I'm pretty sure the answer is the vertex of the function, which I got 20 for but I'm not totally sure.
A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t2 + 640t. After how many seconds does the projectile take to reach its maximum height?

Answer 4

You can use the vertex formula to figure out the max height:

\(t = -\dfrac{b}{2a}\)

\(t = -\dfrac{640}{2(-16)}\)

\(t = 20\)

Next you'll need to insert t = 20 into the given equation:

h(20) = - 16(20)^2 + 640(20)

Answer 5

then simplify the expression on the right to solve for h(20)

Answer 6

@Hero how would you self for h(20)

Answer 7

*solve