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Write the equation of each parabola in vertex form a. Vertex: (-3, 7); Point:(-2, -5) b. Vertex: (1, 3); Point: (2, 5) c. Vertex: (-4, 6); Point: (-2, -2) d. Vertex: (7, 4); Point: (5, 16)

Respuesta :

tramserran

Answer: a) y = 2(x + 3)² - 7

              b) y = -2(x + 4)² + 6

              c) y = 3(x - 7)² + 4

Step-by-step explanation:

The vertex form of a quadratic equation is:  y = a(x - h)² + k     where

  • "a" is the vertical stretch
  • (h, k) is the vertex
  • (x, y) is any point on the curve

Input (h, k) and (x, y) to solve for "a"

a)  (h, k) = (-3, 7)   and   (x, y) = (-2, -5)

    -5 = a(-2 + 3)² - 7

     2 = a(1)²

     2 = a

                y = 2(x + 3)² - 7

b)  (h, k) = (1, 3)   and   (x, y) = (2, 5)

    5 = a(2 - 1)² + 3

     2 = a(1)²

     2 = a

                y = 2(x - 1)² + 3

c)  (h, k) = (-4, 6)   and   (x, y) = (-2, -2)

    -2 = a(-2 + 4)² + 6

    -8 = a(2)²

    -8 = 4a

    -2 = a

                y = -2(x + 4)² + 6

d)  (h, k) = (7, 4)   and   (x, y) = (5, 16)

    16 = a(5 - 7)² + 4

    12 = a(-2)²

     12 = 4a

      3 = a

                y = 3(x - 7)² + 4

xero099

a) The equation of the parabola is [tex]y+3 = -12\cdot (x-7)^{2}[/tex].

b) The equation of the parabola is [tex]y-3 = 2\cdot (x-1)^{2}[/tex].

c) The equation of the parabola is [tex]y-6 = -2\cdot (x+4)^{2}[/tex].

d) The equation of the parabola is [tex]y-4 = 3\cdot (x-7)^{2}[/tex].

The equation of the parabola in vertex form is described below:

[tex]y-k = C\cdot (x-h)^{2}[/tex] (1)

Where:

  • [tex]x[/tex] - Independent variable.
  • [tex]y[/tex] - Dependent variable.
  • [tex]h,k[/tex] - Vertex coordinates.
  • [tex]C[/tex] - Vertex constant.

The vertex constant is found by (1):

[tex]C = \frac{y-k}{(x-h)^{2}}[/tex]

Now we proceed to determine each equation of the parabola:

a) (h, k) = (-3, 7), (x, y) = (-2, -5)

[tex]C = \frac{-5-7}{(-2+3)^{2}}[/tex]

[tex]C = -12[/tex]

The equation of the parabola is [tex]y+3 = -12\cdot (x-7)^{2}[/tex].

b) (h, k) = (1, 3), (x, y) = (2, 5)

[tex]C = \frac{5-3}{(2-1)^{2}}[/tex]

[tex]C = 2[/tex]

The equation of the parabola is [tex]y-3 = 2\cdot (x-1)^{2}[/tex].

c) (h, k) = (-4, 6), (x, y) = (-2, -2)

[tex]C = \frac{(-2-6)}{(-4+2)^{2}}[/tex]

[tex]C = -2[/tex]

The equation of the parabola is [tex]y-6 = -2\cdot (x+4)^{2}[/tex].

d) (h, k) = (7, 4), (x, y) = (5, 16)

[tex]C = \frac{(16-4)}{(5-7)^{2}}[/tex]

[tex]C = 3[/tex]

The equation of the parabola is [tex]y-4 = 3\cdot (x-7)^{2}[/tex].

We kindly invite to check this question on parabolas: https://brainly.com/question/8495869

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