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3 years ago

Write the equation of the following graph in vertex form.

Mathematics

1 answer:

Marat540 [252]3 years ago

6 0

Answer:

Correct choice is 2. $f(x)=0.4(x+2)(x-5)$

Step-by-step explanation:

We have been given a graph of the quadratic function. Now we need to use that graph to find the equation of the graph in vertex form. By the way given choices written in intercept form so to be accurate we are going to find the equation in intercept form.

from graph we see that x-intercepts are at 5 and -2.

we know that if x=a is x-intercept then (x-a) must be factor.

So (x+2)(x-5) is the factor.

when leading coefficient is positive then graph opens upward.

so that means leading coefficient is 0.4

Hence correct choice is 2. $f(x)=0.4(x+2)(x-5)$

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Answer:

If Andrew works for 30 for $4 he will have a total wage of 30×4=$120

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Answer:

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2 years ago

Find the length of the line PA.

Diano4ka-milaya [45]

RO divides the rectangle into two congruent right triangles.

The area of the one triangle is equal half area of the rectangle.

Calculate the area of rectangle:

$A_R=lw\\l=12,\ w=5\\\\A_R=12\cdot5=60$

The area of right triangle:

$A_T=\dfrac{1}{2}A_R\to A_T=\dfrac{1}{2}\cdot60=30$

Use the Pythagorean theorem to calculate the length of RO:

$|RO|^2=5^2+12^2\\\\|RO|^2=25+144\\\\|RO|^2=169\to|RO|=\sqrt{169}\to|RO|=13$

The formula of an area of this right triangle is:

$A_T=\dfrac{1}{2}|RO||PA|$

Therefore we have the equation:

$\dfrac{1}{2}(13)|PA|=30\qquad|\cdot2\\\\13|PA|=60\quad|:13\\\\|PA|=\dfrac{60}{13}\\\\|PA|\approx4.62$

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