All categories

3 years ago

Use the graph of f(x) = x2 to write an equation for the function represented by each graph.

Mathematics

1 answer:

MariettaO [177]3 years ago

7 0

Answer:

y = -(x + 2)² + 1

Step-by-step explanation:

Parent function given in the graph is a quadratic function,

f(x) = x²

Since, graph is opening downwards transformed function of the preimage will be,

g(x) = -x²

This transformed function is shifted further by 2 units left horizontally and 1 unit upwards.

Therefore, rule for the transformation will be,

g(x) → h[(x + 2), (y + 1)]

By this rule transformed function will be,

h(x) = -(x + 2)²+ 1

Equation of the curve will be,

y = -(x + 2)² + 1

You might be interested in

The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

3 years ago

0.85 in fractional notation

artcher [175]

If you would like to write 0.85 in a fractional notation, you can do this using the following steps:

0.85 = 85/100 which simplifies to 17/20 <span>(the common factor of 85 and 100 is 5, so you can divide both numbers by 5).

The correct result would be 17/20.</span>

8 0

3 years ago

Read 2 more answers

Please help me out if possible!

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

Hi,

So lets answer this question;

Here we know that:

69° + z = 180° [Straight angle or Supplementary angle]

⇒ z = 180° - 69°

= <u>111°</u>

3 0

3 years ago

Patty made a banner that has an area of 175 square inches. The length and width of the banner are whole numbers. The length is 7

Leviafan [203]

Answer:

Length = 35

w = 5

Step-by-step explanation:

l x w = area

7y x y = 175

7y^2 = 175

y^2 = 175/7

y^2=25

y=5

The length is 7y, so it's 5 times 7 or 35.

The width is just y, so it's 5.

6 0

2 years ago

The team's combined score was 0. What was Travis's score

Pavlova-9 [17]

Answer:

Sorry but we need more info.

Step-by-step explanation:

8 0

3 years ago