Respuesta :

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

mhanifa

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