Question

WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER + 100 POINTS WHEN YOU DO ANSWER!!
Hello, below I have a screenshot of the question I need to be answered in particular. I would also like to have an explanation as to how you got the answers you did please. I will move on to try other questions whilst I wait, to see if I may be able to do something different without getting stuck again. Thank you for your time and I hope you have/had a good day(or night)!

Answer 1

Answer:

y=-2x²+4x+9

Step-by-step explanation:

Firstly, we need to know the general formula of a quadratic, given by:

$y=ax^2+bx+c$

We need to form three equations with the coordinates we were given, and then we will find each variable.

The three coordinates given,

(4,-7) (-5-61) (-3, -21)

We can begin using (4,-7)

So, plugging those values in, we get

-7= a(4²)+b(4)+c

-7=16a+4b+c

Let's remember this equation and come back to it later.

Secondly, we will use (-5,-61)

-61= a(-5²)+b(-5)+c

-61=25a-5b+c

Again, let's remember this and move onto our last one.

(-3, -21)

-21=a(-3²)+b(-3)+c

-21=9a-3b+c

Now, we have three equations with three variables, so we can use the system of equations to solve for each one.

-7=16a+4b+c

-61=25a-5b+c

-21=9a-3b+c

By solving the system of equations, we eventually get

a=-2, b=4 and c=9

Thus,

y=-2x²+4x+9