Question

Could i get some help in next few minutes?

sketch is another part of question but not necessary

Answer 1

• y=3x²+18x-48
• y=x²+6x-16
• y=(x+8)(x-2)

Zeros:-

• x=-8 and 2

#Vertex

• y=x²+6x-16
• y=x²+2(3x)-16+25-25
• y=x²+2(3x)+9-25
• y=(x+3)²-25

Multiply 3 which we deduced

• y=3(x+3)²-75

Vertex (-3,-75)

Answer 2

• a) - 8 and 2
• b) (- 3, - 75)

Explanation:

Given relation

• y = 3x² + 18x - 48

a)

Find its zero's

• 3x² + 18x - 48 = 0
• x² + 6x - 16 = 0
• x² + 8x - 2x - 16 = 0
• x(x + 8) - 2(x + 8) = 0
• (x + 8)(x - 2) = 0

• x + 8 = 0 ⇒ x = - 8
• x - 2 = 0 ⇒ x = 2

b)

The vertex of qudratic function is determined at x = - b/(2a)

Applied to this relation, the x- coordinate of vertex is

• x = - 18/(3*2) = - 18/6 = - 3

Find its y- coordinate

• y = 3(-3)² + 18(-3) - 48 = 27 - 54 - 48 = -75

The vertex is (- 3, - 75)