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Write the function ????(x) = −2x^2 − 20x − 53 in completed-square form. Describe the transformations of the graph

siniylev [52]

Answer:

The graph of parent function reflected across x-axis, vertically stretched by factor 2 and shift 5 units left 3 units down.

Step-by-step explanation:

The parent function is

$f(x)=x^2$

The given function is

$g(x)=-2x^2-20x-53$

$g(x)=-2(x^2+10x)-53$

If an expression is $x^2+bx$ , then we have to add $(\frac{b}{2})^2$ in it to make it perfect square.

In the parenthesis the value of b is 10.

$(\frac{10}{2})^2=5^2=25$

Add and subtract 25 in the parenthesis.

$g(x)=-2(x^2+10x+25-25)-53$

$g(x)=-2(x^2+10x+25)-2(-25)-53$

$g(x)=-2(x+5)^2+50-53$

$g(x)=-2(x+5)^2-3$

$g(x)=-2f(x+5)-3$ .... (1)

The translation is defined as

$g(x)=kf(x+a)+b$ .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.

Negative k represents the reflection across x-axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (1) and (2) it is clear that k=-2, a=5 and b=-3.

It means graph of parent function reflected across x-axis, vertically stretched by factor 2 and shift 5 units left, 3 units down.

3 0

4 years ago

If you are solving the equation 1/(x-4)+1=14/(x+2) by factoring, which of the following equations would you use the zero product

Grace [21]

Answer:

The equation that would be used for the zero product property on will be (x-5)(x-10)=0

Option B is correct.

Step-by-step explanation:

We need to solve the equation $\frac{1}{(x-4)}+1=\frac{14}{x+2}$

Solving the equation:

$\frac{1}{(x-4)}+1=\frac{14}{x+2}\\\frac{1+(x-4)}{x-4}= \frac{14}{x+2}\\\frac{1+x-4}{x-4}= \frac{14}{x+2}\\\frac{x-3}{x-4}= \frac{14}{x+2}\\Cross\: Multiply\\(x-3)(x+2)=14(x-4)\\x(x+2)-3(x+2)=14x-56\\x^2+2x-3x-6=14x-56\\x^2-x-6-14x+56=0\\x^2-x-14x-6+50=0\\x^2-15x+50=0$

Now, we would factorise to find value of x

$x^2-15x+50=0\\x^2-5x-10x+50=0\\x(x-5)-10(x-5)=0\\(x-5)(x-10)=0$

So, the equation that would be used for the zero product property on will be (x-5)(x-10)=0

Option B is correct.

7 0

3 years ago

Read 2 more answers

A box contains fifteen billiard balls, numbered 1 through 15. Anna draws a ball, records the number, and then returns it to the

Drupady [299]

The correct end part of the question says;

Find the probability of rolling an even number "then" an odd number

Answer:

Probability of rolling even, then odd = 56/225

Step-by-step explanation:

Now, the numbers are from 1 to 15.

Since we want find probability of even, then odd number, let's list all the even numbers first;

Even numbers from 1 to 15 are;

2, 4, 6, 8, 10, 12, 14

Odd numbers from 1 to 15 are;

1, 3, 5, 7, 9, 11, 13, 15

So, we have 7 even numbers and 8 odd numbers.

Probability of even is = 7/15

Probability of odd is = 8/15

Thus,probability of rolling even, then odd is;

P(even, then odd) = 7/15 x 8/15 = 56/225

6 0

4 years ago

Graph m=3 b=-1 m=-2 b=4

Fittoniya [83]

Answer:

y= 3x − 4

Step-by-step explanation:

The slope-intercept form for a linear equation is

y= mx + b, where m = the slope, and b = the y-intercept.

Given:

m= 3 and b = −4

y= 3x - 4

6 0

3 years ago

Simplify the product using FOIL (4x-3)(3x+5)

Sphinxa [80]

$(4x-3)(3x+5) \\ \\ 12x^2 + 20x - 9x - 15 \\ \\ 12x^2 + 11x - 15 \\ \\$

The final result is: 12x<span>² + 11x - 15</span>

8 0

3 years ago