Determine an equation of a quadratic function with x intercepts of -3 and 5 that passes through the point a(4,-21)

y = 21x + -105 or y = 21x - 105

Step-by-step explanation:

Our equation is going to be in the format of y = mx+b, where m is the slope, and b is the y-intercept.

For this, you can find the slope by doing

(y₁-y₂)÷(x₁-x₂)

So we just sub in one of the x intercept points and the point that we already have, so let's do (-21-0)/(4-5). That is equal to 21, therefore, 21 is our slope.

So we have y = 21x + b, so now we can sub in one of our points for y and x in the equation. Let's do (4,-21).

-21 = 21(4) + b

-21 = 84 + b

-105 = b

So our equation is y = 21x + -105, meaning we have a slope of 21 and a y intercept of -105.

Edit: you can also do y = 21x - 105

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!