Question

Find the vertex of each parabola​

Answer 1

Answer: 16) Vertex = (3, 39)

17) Vertex = (-2, -17)

Explanation:

When given the standard form of a quadratic equation: ax² + bx + c

use the Axis of Symmetry formula to find the x-value of the vertex. x = -b/(2a)

Then plug the x-value into the given equation to find the y-value.

16) y = -x² + 6x + 30

↓ ↓ ↓

a= -1 b=6 c=30

`\text{AOS:}\quad x=(-b)/(2a)\quad =(-(6))/(2(-1))\quad =(-6)/(-2)\quad =3`

Max: y = -(3)² + 6(3) + 30

= -9 + 18 + 30

= -9 + 48

= 39

Vertex: (3, 39)

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17) y = 3x² + 12x - 5

↓ ↓ ↓

a= 3 b=12 c= -5

`\text{AOS:}\quad x=(-b)/(2a)\quad =(-(12))/(2(3))\quad =(-12)/(6)\quad =-2`

Min: y = 3(-2)² + 12(-2) - 5

= 3(4) - 24 - 5

= 12 - 29

= -17

Vertex: (-2, -17)