Find the x-intercept of a porabola with a vertex of (-3,-14) and y-intercept (0,-13)

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (- 3, - 14), thus

y = a(x + 3)² - 14

To find a substitute (0, - 13) into the equation

- 13 = 9a - 14 ( add 14 to both sides )

9a = 1 ( divide both sides by 9 )

a = , hence

y = (x + 3)² - 14 ← equation of parabola

To find the x- intercepts let y = 0

(x + 3)² - 14 = 0

Multiply through by 9

(x + 3)² - 126 = 0 ( add 126 to both sides )

(x + 3)² = 126 ( take the square root of both sides )

x + 3 = ± = ± 3

Subtract 3 from both sides

x = - 3 ± 3

The x- intercepts are therefore

x = - 3 - 3 ≈ - 14.22 ( to 2 dec. places ) or

x = - 3 + 3 ≈ 8.22 ( to 2 dec. places )

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

yes the data was not prsented

step-by-step explanation: