All categories

3 years ago

Find the equation of a quadratic function in general form whose graph has points: (-2, 3) (0, 3) and (-4,-5).

Mathematics

1 answer:

Burka [1]3 years ago

7 0

Answer:

-x²-2x+3

Step-by-step explanation:

The first thing I noticed is that the first and second point has the same y intercept despite being only 2 x coordiantes away. This must mean that the vertex's x coordiante is probably (-1,4)

Because the vertex is probably (-1,4) the graph must also be concave down because the point (-4,-5) is below it

writing this in vertex form we get

-a(x+1)²+4

Where a is some constant

solve for a by plugging in (0,3)

3= -a(0+1)²+4

3= -a+4

-1= -a

a=1

therefore the equation looks like

-(x+1)²+4

expanding this so that it's in stantard form...

-(x²+x+x+1)+4

-x²-2x+3

which is the final answer

You might be interested in

What is the smallest whole number that can be multiplied by 300 such that the product is a perfect cube?

Neko [114]

300=2×2×5×5×3

We observe that 2 and 5 are grouped in pairs and the 3 is left unpaired.

If we multiply 300 by the factor 3 then

300×3=2×2×5×5×3×3

900=2×2×5×5×3×3 which is a perfect square.

∴ Required number is 3

root of 900 =30

5 0

3 years ago

Read 2 more answers

Find the factor pairs of each number. 30

nata0808 [166]

To determine the factor pairs for the number 30, simply find out the smallest set of numbers that will multiply to give 30, you would need to break down composite numbers to do this.

30 = 6 • 5 = 2 • 3 • 5.

These all are prime numbers that when multiplied together equals 30.

6 0

4 years ago

At a particular restaurant, each chicken wing has 75 calories and each slider has 250 calories. A combination meal with chicken

VikaD [51]

Know a are:

CW=75. SL= 250. Y= 2x

CW= X= number of wings

SL= Y= number of sliders

X+Y= Total number of items, which can be rewritten as X+2X= total

Plug in the calories for the total

2(75X) +250X= 800

150x+250X= 400X= 800

X= 800/400=2 pieces of Slider

Double the amount for Wings=2x2=4

4wings/2 Sliders

8 0

3 years ago

0.08 ten Times as much as

Shkiper50 [21]

0.008 x10 = 0.08
Answer : 0.008

5 0

3 years ago

Read 2 more answers

Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail inste

Vladimir [108]

Answer:

The value of t test statistics is 5.9028.

We conclude that the true mean is greater than 10 at the .01 level of significance.

Step-by-step explanation:

We are given that a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead.

The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.

Let $\mu$ = true mean transmission of pages.

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 10 pages {means that the true mean is smaller than or equal to 10}

Alternate Hypothesis, $H_A$ : $\mu$ > 10 pages {means that the true mean is greater than 10}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = 14.44 pages

s = sample standard deviation = 4.45 pages

n = sample of fax transmissions = 35

So, test statistics = $\frac{14.44-10}{\frac{4.45}{\sqrt{35} } }$ ~ $t_3_4$

= 5.9028

(a) The value of t test statistics is 5.9028.

Now, at 0.01 significance level the z table gives critical values of 2.441 at 34 degree of freedom for right-tailed test.

Since our test statistics is more than the critical values of z as 5.9028 > 2.441, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true mean is greater than 10.

(b) Now, P-value of the test statistics is given by the following formula;

P-value = P( $t_3_4$ > 5.9028) = Less than 0.05% {using t table)

7 0

3 years ago