Question

Vertex represents a maximum or minimum point for the function. Explain your

answer.
b. Rewrite f(x) in vertex form by completing the square.
2. A cannonball is shot from the top of an ocean cliff as shown. The height (in meters) of the cannonball above th
water is given by h(t) = -5t2 + 15t + 8, where t is the number of seconds after the shot. Determine
whether each statement is true according to the graph. Select True or False for each statement.
Statement
True
Fal
The cannon is 8 meters above the water.
The cannonball reaches its maximum height at 1.5
seconds after it is shot.
The cannonball hits the water 8 seconds after it is
shot.

Answer 1

the vertex represents a maximum

Vertex is (4,7)

f(x)=-(x-4)^2+7

Explanation:

Given the function
`f(x)=-x^2+8x+9`

Equation is in the form of y=ax^2+bx+c

`a=-1`

When 'a' is negative, then vertex is maximum

when 'a' is positive, then vertex is minimum

`a=-1` is negative, so the vertex represents a maximum

`f(x)=-x^2+8x+9`, factor out negative

Take out negative sign in common