Question

The graph represents a cubic function. Write the function.

Answer 1

Zeros are

• (0,0)
• (-3,0)
• (-4,0)

Write in factor form and solve

• (x-0)(x-(-3))(x-(-4))=0
• x(x+3)(x+4)=0
• x[x(x+4)+3(x+4)]=0
• x(x²+4x+3x+12)=0
• x(x²+7x+12)=0
• x³+7x²+12x=0

Points given (-2,16)

Solve for n

• n(x³+7x²+12x)=y

On solving we get

• n=-4

So the function is

• y=-4(x³+7x²+12x)
• y=-4x³-28x²-48x

Answer 2

Answer:

-4x³ - 28x²- 48x

Explanation:

• x-intercept: (-4, 0), (-3, 0), (0, 0)

→ so equation: a(x+4)(x+3)(x+0)

• point given: (-2, 16)

→ substitute these points to find a

• a(-2+4)(-2+3)(-2) = 16

• a = -4

so the graphed cubic equation:

• -4(x+4)(x+3)(x+0)

• -4x³ -28x²-48x