ALGEBRA 2 *need work to be shown * solve the following equation x^2 + 27=-9
2 answers:
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Answer:
1
Step-by-step explanation:
y-intercept is defined as the point where the graph crosses the y-axis. The value of x coordinate at this point is zero, as along entire y-axis, the value of x coordinate is always zero. So substituting x = 0 in the function will give us the y-coordinate of the y-intercept of the given function.
Substituting x = 0 in this function, we get:
Thus, the y-coordinate of the y-intercept is 1. Therefore the y-intercept of the function in ordered pair will be: (0, 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
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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.
