Question

Find the vertex of each parabola​

Answer 1

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

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

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

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

Min: y = 3(-2)² + 12(-2) - 5

          = 3(4) - 24 - 5

          = 12 - 29

          = -17

Vertex: (-2, -17)