Find the vertex of the graph of the following quadratic equations y=2x^2-8x+9

What is the equation of the axis of symmetry for the function shown below?

Gennadij [26K]

Answer:

x=2

Step-by-step explanation:

The axis of symmetry can be calculated using the following formula:

$Xv= \frac{-b}{2a}$

In order to use this formula, we need to have the function written in it's polynomial formula:

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

In order to do so, we have to isolate Y from the excercise's formula.

$y=-2(x-2)^2-5$

Then we resolve the square of the binomial knowing that (a+b)^2=a^2+2.a.b+b^2

$(x-2)^2= x^2+2.x.(-2)+(-2)^2$

$(x-2)^2= x^2-4x+4$

Now we have that:

$y=-2.(x^2-4x+4)-5$

$y=-2x^2+8x-8-5$

$y=-2x^2+8x-13$

As we have now the polynomyal formula, we know that a=-2, b=8 and c=-13. We supplant on the formula and get:

$Xv= \frac{-b}{2a}$

$Xv= \frac{-8}{2.(-2)}$

$Xv= \frac{-8}{-4)}$

$Xv= 2$

4 0

4 years ago

Two arcades have different pricing structures. Arcade A costs $5 to enter and $0.60 per game. Arcade B costs $7 to enter and $0.

WARRIOR [948]

Answer:

10 games

Step-by-step explanation:

Let C be cost and x be number of games

Arcade A: C = 5 + 0.6x

Arcade B: C = 7 + 0.4x

for both arcades to be the same price, Both C's must be equal, hence we equate the right side of both equations:

5 + 0.6x = 7 + 0.4x (subtract 5 fromboth sides)

0.6x = 7 + 0.4x - 5

0.6x = 2 + 0.4x (subtract 0.4x from both sides)

0.6x - 0.4x = 2

0.2x = 2 (divide both sides by 0.2)

x = 2 / (0.2)

x = 10

7 0

3 years ago

Read 2 more answers

Simplify, write without exponents.

LuckyWell [14K]

it is helpful to you

4 0

3 years ago

1.) How could you describe the pair of lines y = 2x – 5 and 4x – 2y = 9: parallel, perpendicular, or neither?

Verizon [17]

<span>The lines are parallel, but with slightly different y-intercepts. The lines are y=2x-5 and y=2x-4.5 The lines are parallel but one crosses the y-axis at 5 and one crosses the y-axis at 4.5.</span>

6 0

3 years ago

The mean weight of an adult is 69 kilograms with a variance of 121. If 31 adults are randomly selected, what is the probability

amid [387]

Answer:

0.2236 = 22.36% probability that the sample mean would be greater than 70.5 kilograms.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Also, important to remember that the standard deviation is the square root of the variance.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$