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Sagot :
Answer:
i did the first
Step-by-step explanation:
1st way
Standard form: a(X-h)²+k = ( -2/3X² -16/3X -32/3) +32/3 -17/3 = -2/3(X +4)² +5
y = -2/3*X^2-16/3*X-17/3
X = -4 ±√( 15/2) = -6.7386, or -1.2614
Axis of symmetry: X= -4; Vertex (maximum)=(h,k)=( -4, 5); y-intercept is (0,-5.66666666667)
two real roots: X=-1.2613872124776866 and -6.738612787477313
Answer:
- b) y = -2/3(x + 4)² + 5
- c) y = 1/2(x + 8)² - 5
- d) y = 3/8(x + 7)² - 2
Step-by-step explanation:
Vertex form is:
- y = a(x - h)² + k
Vertex of the function is point (h, k)
b) Congruent to y = 2/3x² and opens down means:
- a = -2/3
Maximum value at (-4, 5) means:
- h = -4, k = 5
The function is:
- y = -2/3(x + 4)² + 5
c) Congruent to y = 1/2x² and has minimum value y = -5 at x = -8:
- a = 1/2, h = -8, k = -5
The function is:
- y = 1/2(x + 8)² - 5
d) Vertex (-7, -2) and passes through the point (-3, 4)
- y = a(x + 7)² - 2
Substitute coordinates and find a:
- 4 = a(-3 + 7)² -2
- 6 = 16a
- a = 3/8
The function is:
- y = 3/8(x + 7)² - 2
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