Question

Please help me(20 points will give brainliest!!!)

Answer 1

Answer:

A. Vertex is ( -1, 16)

B. Do they mean y-intercept for vertical intercept? That is (0,14)

C. X-intercepts are

(-3.838, 0) and (1.828, 0)

Step-by-step explanation:

plug the equation into desmos. It will graph and give you the info.

To find y-int, plug in 0 for x. This gives you the point 0, 14.

You can also use the quadratic equation to find the x-intercepts.

Answer 2

Answer:

see explanation

Step-by-step explanation:

A

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - $\frac{b}{2a}$

f(x) = - 2x² - 4x + 14 ← is in standard form

with a = - 2, b = - 4 , then

x = - $\frac{-4}{-4}$ = - 1

substitute x = - 1 into f(x) for corresponding y- coordinate

f(- 1) = - 2(- 1)² - 4(- 1) + 14 = - 2 + 4 + 14 = 16

vertex = (- 1, 16 )

B

to find the y- intercept let x = 0

f(0) = - 2(0)² - 4(0) + 14 = 0 - 0 + 14

y- intercept = (0, 14 )

C

to find the x- intercepts let f(x) = 0 , that is

- 2x² - 4x + 14 = 0 ( divide through by - 2 )

x² + 2x - 7 = 0 ( add 7 to both sides )

x² + 2x = 7

using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(1)x + 1 = 7 + 1

(x + 1)² = 8 ( take square root of both sides )

x + 1 = ± $\sqrt{8}$ ( subtract 1 from both sides )

x = - 1 ± $\sqrt{8}$

then

x = - 1 - $\sqrt{8}$ ≈ - 3.83 ( to 2 dec. places )

x = - 1 + $\sqrt{8}$ ≈ 1.83 ( to 2 dec. places )

that is x- intercepts are (- 3.83, 0 ) , (1.83, 0 )