Write an equation of a parabola in vertex form that passes through (7, -17) and has a vertex (4, 1)

Step-by-step explanation:

f(x) = a(x - h)² + k  - the vertex form of an equation of a parabola with vertex (h, k)

(4, 1)  ⇒  h = 4.   k = 1

f(x) = a(x - 4)² + 1   - the vertex form of an equation of the parabola with vertex (4, 1)

the parabola passes through (7, -17)  ⇒ x=7,  f(x)=-17

-17 = a(7 - 4)² + 1

-17 -1 = a(3)² + 1 -1

-18 = 9a

a = -2

The equation of the parabola in vertex form that passes through (7, -17) and has a vertex (4, 1):

                              f(x) = -2(x - 4)² + 1

the mean and mad

step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)