What is the equation of the quadratic function that has a minimum at (7,-3) and goes through (9,9)

y = 3x^2 - 42x + 144

Step-by-step explanation:

Looking at the information given, the minimum at (7,-3) is also the vertex of the parabola that would be formed if the graph is drawn. This minimum point is represented as (h,k). We will apply the vertex form of forming quadratic equations,

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

h = 7

k = - 3

Substituting Into the equation, it becomes

y = a(x - 7)^2 - 3

To find a, we will use the given point,

(9,9)

We will substitute x =9 and y = 9 into the equation, y = a(x - 7)^2 - 3. It becomes

9 = a(9 - 7)^2 - 3

9 = a × 2^2 - 3

9 = a×4 - 3

4a = 9 + 3 = 12

a= 12/4 = 3

The equation becomes

y = 3(x - 7)^2 - 3

y = 3(x - 7)(x - 7) - 3

y = 3(x^2 - 7x - 7x + 49) - 3

y = 3(x^2 - 14x + 49) - 3

y = 3x^2 - 42x + 147 - 3

y = 3x^2 - 42x + 144

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

b, i believe, but not sure.