Answer: 16) Vertex = (3, 39)
17) Vertex = (-2, -17)
Step-by-step 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
[tex]\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(6)}{2(-1)}\quad =\dfrac{-6}{-2}\quad =3[/tex]
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
[tex]\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(12)}{2(3)}\quad =\dfrac{-12}{6}\quad =-2[/tex]
Min: y = 3(-2)² + 12(-2) - 5
= 3(4) - 24 - 5
= 12 - 29
= -17
Vertex: (-2, -17)
