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Question

write the equation of each parabola in vertex form. write in form y=a(x-p)^2 + q

a) vertex (1,-4) y intercept 2

b) vertwx is (-2,3) congruent to y=2x^2 and opens downward

c) vertex (0,2) passes through the point (-3,11)

Answer 1

(a)

Parabolic equation in vertex form is y=a(x-p)² + q

(p,q) are the vertex of Parabolic function

(1, -4) is the vertex and y intercept 2

Substitute vertex (1, -4), x=0 and y=2  in the equation y = a(x-p)² + q.

2=a(0-1)²  - 4

a=6

Equation of parabola with vertex (1, -4) is y = 6(x-1)² - 4.

Answer 2

(b)

Vertex (-2,3) congruent to y=2x² and opens downwards.

The Equation of parabola with vertex (-2, 3) is y = a(x+2)² + 3

The Congruent Line is y = 2x² from which a=2.

Equation of Parabola is y = 2(x+2)² + 3

Answer 3

(c)

Vertex of the parabola is (0,2)

y = a(x-0)² + 2

y = ax² + 2

This intersects at the point (-3, 11)

11 = a(-3)² + 2

9 = 9a

a = 1.

Therefore Parabolic equation is y = x² + 2.