Explain how the graph of a quadratic function relates to

Mathematics

2 answers:

Alexeev081 [22]3 years ago

8 0

Answer:

The zeros of a quadratic function are the solutions of the related quadratic equation. If the graph of a quadratic function crosses the x-axis, there will be two real number solutions. If the graph of a quadratic function just touches the x-axis, there will be one unique real number, or double root, solution. If the graph of a quadratic function does not cross the x-axis, there will be no real number solution.

Step-by-step explanation:

igomit [66]3 years ago

5 0

The equation for a quadratic is as follows:
y = ax^2+bx+c

The first variable “a” determines whether the parabola opens up or down
The squared allows the equation to look like the parabola swoop when graphed.
The c term is the constant term

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3 years ago

A math professor notices that scores from a recent exam are normally distributed with a mean of 61 and a standard deviation of 8

Alexeev081 [22]

Answer:

a) 25% of the students exam scores fall below 55.6.

b) The minimum score for an A is 84.68.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 61 and a standard deviation of 8.

This means that $\mu = 61, \sigma = 8$

(a) What score do 25% of the students exam scores fall below?

Below the 25th percentile, which is X when Z has a p-value of 0.25, that is, X when Z = -0.675.

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

$-0.675 = \frac{X - 61}{8}$

$X - 61 = -0.675*8$

$X = 55.6$

25% of the students exam scores fall below 55.6.

(b) Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?

This is the 100 - 0.15 = 99.85th percentile, which is X when Z has a p-value of 0.9985. So X when Z = 2.96.

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

$2.96 = \frac{X - 61}{8}$