Question

Look at picture y=_the height of the baseball after 5 seconds is ___ feet​

Answer 1

Answer:

• y = -2(x -3)² +24
• 16 feet

Step-by-step explanation:

We expect the equation for y to be quadratic. Since the table is obviously symmetrical about x=3, we can start with the vertex form ...

  y = a(x -3)² +b

Filling in the values from the first two table points, we get

  For (x, y) = (0, 6):

     6 = a(0 -3)² + b       ⇒   9a +b = 6

  For (x, y) = (2, 22):

     22 = a(2-3)² +b       ⇒   a +b = 22

Subtracting the second equation from the first gives ...

  (9a +b) -(a +b) = (6) -(22)

  8a = -16 . . . . . . collect terms

  a = -2 . . . . . . . . divide by 8

The second equation above tells us ...

  b = 22 -a = 22 -(-2) = 24

So, our equation for y is ...

  y = -2(x -3)² +24

__

The value of y for x=5 is ...

  y = -2(5 -3)² +24 = 16

The height of the ball after 5 seconds is 16 feet.