EZ QUESTION - FREE BRAINLIEST: Write the equation of the parabola that has the vertex at point (−2,7) and passes through the point (−1,3).

Step One

Use the vertex to determine the basic equation for the parabola.

y = a(x - 2)^2 + 7 Notice the sign change for x. I have provided a graph to show how this would look with a = 1 (in red.)

What it means is the  2 has to be minus in order that the vertex will shift 2 units in the x direction.

Step Two

Use the point to solve for a.

y = a(x - 2)^2 + 7

When x = - 1

Then y = 3

3 = a(-1 - 2)^2 + 7                combine -1 with - 2

3 = a (-3)^2 + 7

3 = 9a + 7                            Subtract 7 from both sides

3 - 7 = 9a

-4 = 9a                                 Divide by 9.

a = -4/9

or                                

a = - 0.4444

y = -0.4444(x + 2)^2 + 7 <<<<< answer

y = - 4/9 (x + 2)^2 + 7

Note: if you have choices, list them please.

Note: The red graph is y = (x - 2)^2 + 7 ; a = 1

The blue graph is y = - 4/9(x - 2)^2 + 7 ; a = - 0.44444

1 It widens the graph

jcherry99 avatar

It turns the graph upside down. The next one is the tough one.

jcherry99 avatar

It gives the parabola two real roots.

jcherry99 avatar

If you thought of others, so much the better.

Step-by-step explanation:

y = - 4x² - 16x - 9

Step-by-step explanation:

the equaion 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 ) = (- 2, 7 ) , then

y = a(x + 2)² + 7

to find a substitute (- 1, 3 ) into the equation

3 = a(- 1 + 2)² + 7 ( subtract 7 from both sides )

- 4 = a(1)² = a

then

y = - 4 (x + 2)² + 7 ← in vertex form

   = - 4(x² + 4x + 4) + 7

   = - 4x² - 16x - 16 + 7

   = - 4x² - 16x - 9 ← in standard form

0.02040816326

answer: what are the following choices