Question

Find a quadratic equation for a function y = f(x) which crosses the x-axis at x = -1 and x = 6, and which crosses the y-axis at y = 24.

Answer 1

if a quadratic has roots of -1 and 6 then you can write it as y = c(x + 1)(x - 6) for some constant, c. can you determine what c is?

Answer 2

Is c supposed to be like "a", where a is the amplitude?

Answer 3

i wrote it as just any arbitrary constant. consider y = c(x + 1)(x - 6), now solve for the y-intercept (x = 0) by forcing the y-intercept to be 24. this will give you a unique value of c.

Answer 4

so you would set up that 24=c(x+1)(x-6) ?

Answer 5

yes, and remembering that the y intercept is the point at which x = 0

Answer 6

so c= -4

Answer 7

so now that I've found the constant, what would my next step be?

Answer 8

you're finished.

y = -4(x + 1)(x - 6)

is a quadratic equation that satisfies all of the required conditions. its x-intercepts are -1 and 6, and its y-intercept was shown to be 24. you may expand it if you like

Answer 9

thank you!