Question

Use the method of symmetry to find the extreme value of each quadratic function and the value of x for which it occurs. g(x)=2x^2+14x-16
find x intercepts,
midpoint of x intercepts
whether the extreme value is minimum or maximum
write in g(midpoint)=______

Answer 1

Answer:

g(x) = 2x² + 14x - 16

2x² + 14x - 16 = 0

x² + 7x - 8 = 0

x² - 1 + 7x - 7 = 0

(x - 1)(x + 1) + 7(x - 1) = 0

(x - 1)(x + 8) = 0

x = - 8, x = 1  

1/2(-8 + 1) = -7/2 = - 3.5  

Take minimum as the leading coefficient is positive  and write in g(midpoint):

g(-3.5) = 2(-3.5)² + 14(-3.5) - 16 = - 40.5

The vertex is: (- 3.5, - 40.5)

Answer 2

Step-by-step explanation:

Given function:

• g(x) = 2x² + 14x - 16

Find x intercepts:

• 2x² + 14x - 16 = 0
• x² + 7x - 8 = 0
• x² - 1 + 7x - 7 = 0
• (x - 1)(x + 1) + 7(x - 1) = 0
• (x - 1)(x + 8) = 0
• x = - 8, x = 1

Midpoint of x intercepts:

• 1/2(-8 + 1) = -7/2 = - 3.5

Whether the extreme value is minimum or maximum:

• Its minimum as the leading coefficient is positive

Write in g(midpoint):

• g(-3.5) = 2(-3.5)² + 14(-3.5) - 16 = - 40.5

The vertex is: (- 3.5, - 40.5)