Consider the quadratic equation y = – x 2 – 8 x – 23. What is the vertex? (8, 7)

Question

Consider the quadratic equation y = – x2 – 8x – 23. What is the vertex?

(8, 7)

(4, 25)

(-4, -7)

(-4, 13)

(-8, 23)

Consider the quadratic equation y = x2 – 36. What are the values of the x-coordinates when y equals 28?

2 or -18

4 or -9

6 or -6

8 or -8

16 or -4

The Tennis Superstore makes $2 of profit from each can of tennis balls it sells. The total daily cost associated with the sale of this item today is $90. What is the store’s daily revenue from the sell of 250 cans of tennis balls today?

$660

$590

$500

$430

$410

(8, 7)

(4, 25)

(-4, -7)

(-4, 13)

(-8, 23)

Explanation / Answer

1st Part :

Given :

y = -x2-8x-23

From this equation we can say it represents a parabola as it bears the equation as Ax2+Bx+C

So, coefficients are :

A = -1

B = -8

C = -23

Formula for x-coordinate of the vertex is given by  -B/(2A)

= -(-8)/2(-1)

=-(8/2)

=-4

So x = -4

From this we can calculate the value of y as

y = -x2-8x-23

y= -(-4)2 -8(-4) – 23

y= -16 + 24 -23

y= -15

Therefore, vertex is (-4,-15)

2nd Part :

Given :

y = x2 – 36

when y = 28

28 = x2 – 36

x2 = 28+36 = 64

x = 64

x = +8 or -8

3rd Part:

Given:

Profit for each can of tennis ball = $2

Daily cost (Expense) for the sale = $90

Total cans Sold today = 250

Total Profit earned = $(250 * 2) = $500

Grand Profit after expense = $(500-90) = $410

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.