All categories

2 years ago

What is the vertex of the graph of the function f(x) = x2 + 8x - 2?

Mathematics

1 answer:

vlabodo [156]2 years ago

5 0

Answer:

Vertex is (-4, -18)

Step-by-step explanation:

f(x) = $ax^{2} +bx +c$

Let (h, k) be the vertex

An easy way to find h is to use the formula h = -b/2a

In your case where f(x) = $x^{2} +8x - 2$ a = 2 and b = 8

So, h = -8/2(1) = -8/2 = -4

Substitue -4 in for x to find k

k = ( $-4^{2}$ ) + 8(-4) - 2

= (16) - 32 - 2

= 16 - 32 - 2

= -18

Vertex is (-4, -18)

Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases

You might be interested in

A vendor sells pizza and soft drinks. A customer buys 6 slices of pizza and 5 drinks for $31.60. Another customer buys 5 slices

Irina-Kira [14]

let the price of a slice of pizza be 'p' and that of soft drink be 's'

6 p + 5 s = 31.60............equation (i)
5 p + 4 s = 26.02............equation (ii)

6 p + 5 s = 31.60............×4
5 p + 4 s = 26.02............×5

24 p + 20 s = 126.4
25 p + 20 s = 130.1

p = 3.7

Answer = 3.7 Dollars

6 0

3 years ago

Read 2 more answers

The Atlantic Salmon swim upstream at a steady rate of 2 miles every 3 minutes. Fill in the table to describe the relationship. R

Likurg_2 [28]

The distance traveled by the Salmon is proportional to the duration spent

swimming.

A table of the distance traveled by the Atlantic Salmon is presented as follows;

$\begin{tabular}{|c|c|c}\underline{Time in minutes}&\underline{Miles Traveled at 2/3 miles per minute } \\1&2/3 \\2&4/3\\3&2\\4&8/3\\5&10/3\\6&4\end{array}$

Reasons:

The given parameter are;

The steady rate at which Atlantic Salmon swims = 2 miles in 3 minutes

Distance the Salmon swims, d ∝ Time taken, t

Therefore;

d = s·t

Where;

s = The constant of proportionality = The speed

Which gives;

$\displaystyle s = \mathbf{\frac{Distance, \, d}{Time, \, t}}$

The speed with which the Atlantic Salmon swims per minute is therefore;

$\displaystyle The \ speed = \mathbf{\frac{2 \ miles}{3 \ minutes}} = \frac{2}{3} \ miles /minute$

The distance travelled, <em>d</em>, is given as follows;

$\displaystyle d = \mathbf{\frac{2}{3} \times t}$

A table showing the distance travelled by the fish with time is presented as follows;

$\begin{tabular}{|c|c|c|}\underline{Time, t, in minutes}&\underline{t \times d}&\underline{Miles Traveled, d, at 2/3 miles per minute } \\1&1 \times 2/3 = 2/3&2/3 \\2&2 \times 2/3 = 4/3&4/3\\3&3 \times 2/3 = 2&2\\4&4 \times 2/3 = 8/3&8/3\\5&5 \times 2/3 = 10/3&10/3\\6&6 \times 2/3 = 4&4\end{array}$