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3 years ago

Which of the following describes the graph of y = x² - 225?

Mathematics

1 answer:

lara [203]3 years ago

3 0

Answer:

option 4. The graph has zeroes at x = 15 an x = -15 and it opens upward.

Step-by-step explanation:

we have

$y=x^{2} -225$

This is the equation of a vertical parabola open upward (the leading coefficient is positive)

The vertex represent a minimum

The vertex is the point (0,-225)

The axis of symmetry is x=0 (y-axis)

Find the x-intercepts (values of x when the value of y is equal to zero)

For y=0

$0=x^{2} -225\\x^2=225$

square root both sides

$x=\pm15$

therefore

The graph has zeroes at x = 15 an x = -15 and it opens upward.

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Simplify the following expression. (4x − 8)(4x + 8)

vitfil [10]

Answer:

16x^2 - 64

Step-by-step explanation:

(4x − 8)(4x + 8)

We recognize that this is the difference of squares

(a-b) (a+b) = a^2 - b^2

=(4x)^2 - 8^2

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3 years ago

Use exact numbers. Complete the equation of the line through ( 2 , 1 ) (2,1)left parenthesis, 2, comma, 1, right parenthesis and

Anastasy [175]

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

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To find c substitute either of the 2 points into the partial equation

Using (2, 1) , then

1 = - 6 + c ⇒ c = 1 + 6 = 7

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Answer:

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Step-by-step explanation:

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$\therefore \: ( - 5 \: - 12) = (x \: y) \\ r = \sqrt{ {x}^{2} + {y}^{2} } \\ = \sqrt{ {( - 5)}^{2} + {( - 12)}^{2} } \\ = \sqrt{25 + 144} \\ = \sqrt{169} \\ r= 13 \\ \\ \sin \theta = \frac{y}{r} = - \frac{12}{13} \\ \\ \cos \theta = \frac{x}{r} = - \frac{5}{13} \\ \\ \tan \theta = \frac{y}{x} = \frac{ - 12}{ - 5} = \frac{12}{5} \\ \\ \csc \theta = \frac{r}{y} = - \frac{13}{12} \\ \\ \sec \theta = \frac{r}{x} = - \frac{13}{5} \\ \\ \cot \theta = \frac{x}{y} = \frac{ - 5}{ - 12} = \frac{5}{12}$

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