WRITE QUADRATIC EQUATION WITH VERTEX AND POINT

Write an equation of the parabola in intercept form.

Problem 1 :

Solution:

Intercept form:

y = a(x - p)(x - q)

p = 2 and q = 4

y = a(x - 2)(x - 4)

Vertex (x, y) = (3, 4)

4 = a(3 - 2)(3 - 4)

4 = a(1)(-1)

4 = -a

a = -4

y = -4(x - 2)(x - 4)

Problem 2 :

Solution:

Intercept form:

y = a(x - p)(x - q)

p = -1 and q = 2

y = a(x + 1)(x - 2)

Vertex (x, y) = (1, -2)

-2 = a(1 + 1)(1 - 2)

-2 = a(2)(-1)

-2 = -2a

a = 1

y = 1(x + 1)(x - 2)

Problem 3 :

x-intercepts of 12 and -6; passes through (14, 4)

Solution:

Intercept form:

y = a(x - p)(x - q)

p = 12 and q = -6

y = a(x - 12)(x + 6)

It passes through the point (x, y) = (14, 4).

4 = a(14 - 12)(14 + 6)

4 = a(2)(20)

4 = 40a

a = 1/10

y = 1/10(x - 12)(x + 6)

Problem 4 :

x-intercepts of 9 and 1; passes through (0, -18)

Solution:

Intercept form:

y = a(x - p)(x - q)

p = 9 and q = 1

y = a(x - 9)(x - 1)

It passes through the point (x, y) = (0, -18).

-18 = a(0 - 9)(0 - 1)

-18 = a(-9)(-1)

-18 = 9a

a = -2

y = -2(x - 9)(x - 1)

Problem 5 :

x-intercepts of -16 and -2; passes through (-18, 72)

Solution:

Intercept form:

y = a(x - p)(x - q)

p = -16 and q = -2

y = a(x + 16)(x + 2)

It passes through the point (x, y) = (-18, 72).

72 = a(-18 + 16)(-18 + 2)

72 = a(-2)(-16)

72 = 32a

a = 9/4

y = 9/4(x + 16)(x + 2)