Question

HELP PLEASE!!!

Answer 1

A)The x-intercepts are at x=-2 and x=-4; the y-intercept is at y=8.
B) Vertex form is g(x) = -2(x-2)²+11, and the axis of symmetry is at x=2.
C) It takes 1.75 seconds for the dolphin to complete one jump.

Explanation:
A) To find the x-intercepts, we replace y (in this case, f(x)) with 0 and solve:
0 = (x+3)²-1

First, add 1 to both sides:
0+1 = (x+3)²-1+1
1 = (x+3)²

Take the square root of both sides:
√1 = √(x+3)²
+/- 1 = x+3

Subtract 3 from both sides:
-3 +/- 1 = x

This means x=-3-1 and x=-3+1, or x=-4 and x=-2.

B)  To write g(x) in vertex form, we must complete the square.  First we will factor the GCF of the first two terms out:
g(x) = -2(x²-4x)+3

To find the value that we add (and subtract, to maintain equality) to this function, we take half of the value of b (the one in parentheses) and square it:
(-4/2)²=(-2)²=4

This is what we will add in parentheses.  Since this will be multiplied by -2, this means to cancel it, we will add 8 as well (2*-4 = -8; -8+8=0):
g(x)=-2(x²-4x+4)+3+8
g(x)=-2(x²-4x+4)+11

Factoring the trinomial in parentheses, we have
g(x) = -2(x-2)²+11.

The axis of symmetry is given by x = -b/2a:
x = -8/2(-2) = -8/-4 = 2

C)  We will set this equal to 0 to solve it:
0 = -16t² + 28t

Now we will factor out the GCF, 4t:
0 = 4t(-4t+7)

Using the zero product property, we know that either 4t=0 or -4t+7=0:
4t=0

Divide both sides by 4:
4t/4 = 0/4
t = 0

This is when the dolphin first jumps.

-4t+7=0

Subtract 7 from both sides:
-4t+7-7=0-7
-4t = -7

Divide both sides by -4:
-4t/-4 = -7/-4
t = 7/4 = 1.75