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3 years ago

Instructions: Given the vertex of a quadratic function, find the axis

Mathematics

1 answer:

allsm [11]3 years ago

5 0

The axis of symmetry is x = 5.

In first place, every quadratic function can be expressed as follows:

f(x) = a*x² + b*x + c

where a, b and c are real numbers and a ≠ 0. This way of writing the quadratic function is called polynomial.

The graph of a quadratic function is a parabola. Every parabola is a symmetric curve with respect to a horizontal line called the axis of symmetry. That is, the axis of symmetry is an imaginary line that passes through the middle of the parabola and divides it into two halves that are mirror images of each other.

The point of intersection of the axis of symmetry with the parabola is called the vertex, and it divides the parabola into two branches. That is, the axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Then, being the vertex of the quadratic function (5,7), where the vertex on the x-axis has a value of 5 and on the y-axis a value of 7, the axis of symmetry is x = 5.

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Step-by-step explanation:

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The CEO of the Jen and Benny's ice cream company is concerned about the net weight of ice cream in their 50 ounce ice cream tubs

MissTica

Answer:

$t=\frac{54.98-52}{\frac{8.43}{\sqrt{26}}}=1.8025$

We need to find the degrees of freedom given by:

$df = n-1= 26-1 = 25$

Since is a right tailed test the p value would be:

$p_v =P(t_{25}>1.8025)=0.0418$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the average is higher than 52 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=54.98$ represent the sample mean

$s=8.43$ represent the sample deviation

$n=26$ sample size

$\mu_o =52$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 52, the system of hypothesis would be:

Null hypothesis: $\mu \leq 52$

Alternative hypothesis: $\mu > 52$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{54.98-52}{\frac{8.43}{\sqrt{26}}}=1.8025$

P-value

We need to find the degrees of freedom given by:

$df = n-1= 26-1 = 25$

Since is a right tailed test the p value would be:

$p_v =P(t_{25}>1.8025)=0.0418$

Conclusion

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