Question

Find a formula for the quadratic function depicted in the following graph.

Answer 1

@vocaloid

Answer 2

The vertex form of a quadratic equation is

y = a(x - h)^2 + k

where (h, k) is the vertex
and a is a constant

what is the vertex in your graph?

Answer 3

i can't say

Answer 4

How about now? Can you figure out what the vertex is

Answer 5

(-4, -4) if i'm not mistaken

Answer 6

uhh what is this point?

Answer 7

-1

Answer 8

am i right

Answer 9

that's not the x-coordinate nor is it the y-coordinate

Answer 10

(1, -4)

Answer 11

There you go, now replace it in the vertex form I shared above and you'll get

y = a(x-1)^2 - 4

and now to find out the value of a, just plug in a point from the graph and solve for a

For example, the point (0, -4)

Answer 12

My bad, the point on the graph is (0, -3)

y = a(x-1)^2 - 4

so if you plug in the point (0, -3)
x = 0 and y = -3

What does a = ?

Answer 13

-3 = a(0-1)^2 - 4

a = 1

Answer 14

?

Answer 15

Exactly so now that you know a = 1

and that the vertex is (1, -4) so h = 1 and k = -4

What is the formula for the quadratic function?

Answer 16

y = a(x - h)^2 + k

f(x) = (1x2)^2 + 1 + -4

Answer 17

is this right ?

Answer 18

You have to keep the numbers together

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

and 1 outside of the parenthesis multiplied by that changes nothing so it's simply f(x) = (x-1)^2 - 4

If you want, you can simplify it by expanding (x-1)^2 and adding/subtracting any like terms. That's probably the answer they'd want you to submit

Answer 19

f(x) = (x-1)^2 - 4 is right , thank you

Answer 20

No problem!