Answer:
16. b.
17. b.
Step-by-step explanation:
16.
Since you are given the x-intercepts of the parabola, use the x-intercept form equation: y = a(x-s)(x-r)
-s and -r are the x-intercepts. Notice that they are negatives in the equation. This means when you put the x-intercepts into the formula, you have to change whether they are negative or positive.
Given x-intercepts 2 and -8, the equation is:
y = a(x-2)(x+8)
Substitute the point (-6,-4). You do not need to change negative/positive
-4 = a(-6-2)(-6+8) simplify
-4 = a(-8)(2)
-4 = -16a divide both sides by -16 to isolate "a"
a = -4/-16 reduce the fraction
a = 1/4
Substitute a= 1/4 back to get the equation
y = 1/4(x-2)(x+8)
17.
Since you are given the vertex, use vertex form: y = a(x-h)²+k
The vertex is (-h, k). You only need to change the negative/positive for the x-coordinate.
Given vertex (2, 3), the equation is y = a(x-2)²+3.
The focus is on the line of symmetry of the parabola and is inside the parabola. Since the parabola opens down, the focus in below the vertex.
Because the vertex is 3 units away from the focus, reduce the y-coordinate by 3.
(2,3) becomes (2, 0).
The focus is (h, k+p) and p is (1/4a).
The focus y-coordinate is k+p, and it's also 0. k is 3, the y-coordinate of vertex.
Sub k=3 and k+p=0 for the y-coordinate of the focus.
3 + p = 0
p = -3
Substitute p=3 to find "a"
p = 1/4a
-3 = 1/4a
1 = (4a)(-3) simplify
1 = -12a divide both sides by -12 to isolate "a"
a = 1/-12
Now we can find the equation by substituting a= -1/12 into the formula.
y = -1/2(x-2)²+3
