Question

Algebra 2 Honors Unit 7 RETAKE ZOOM 2. Find the leading coefficient (a) of the cubic function that has roots at -9, -5, and 3 with a y-intercept of -27. Round answer to hundredth's place (2 decimal places)​

Answer 1

Answer:

To find the cubic function with the given roots, we can use the factored form of a cubic function:

f(x) = a(x - r1)(x - r2)(x - r3)

where r1, r2, and r3 are the roots of the function.

Substituting the given roots, we get:

f(x) = a(x + 9)(x + 5)(x - 3)

To find the leading coefficient a, we need to use the y-intercept of the function, which is given as -27.

When x = 0, the function becomes:

f(0) = a(9)(5)(-3) = -27

Simplifying and solving for a, we get:

a = -27 / (9)(5)(-3) = 0.6

Rounding to two decimal places, the leading coefficient of the cubic function is a = 0.60.