WILL GIVE BRAINLIEST

1. Find the vertex of the following: y = (x - 4)(x - 10) *

horsena [70]

Answer:

1. (7,-9)

2. (4,0) and (10,0)

3. (3,0) and (-3,0)

4. (0,-9)

5. (-1,-32)

Step-by-step explanation:

To find the vertex use the formula

$\frac{-b}{2a}$

First make the equation into a quadratic equation.

$(x-4)(x-10)\\x^{2} -10x-4x+40\\x^{2} -14x+40$

Now it is in the form

$ax^{2} +bx+c=0$

Now we can substitute the values

$\frac{-(-14)}{2(1)} \\\frac{14}{2} \\7$

Now we have 7 as our x value for the vertex we can substitute for y,

$x^{2} -14x+40=y\\(7)^{2} -14(7)+40=y\\49-98+4=y\\y=-9$

So the vertex for 1 is (7,-9)

To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.

$x-4=0\\x=4\\\\x-10=0\\x=10$

4 is slightly different but start the same,

$(x-3)(x+3)\\x^{2}+3x-3x-9\\x^{2}-9$

Here, c (9) just shows the graph move down 9, so the y intercept = 9.

5 is the same process as 1,

$2(x-3)(x+5)\\2(x^{2}+5x-3x-15)\\2(x^{2}+2x-15)\\2x^{2}+4x-30$

Vertex,

$\frac{-(4)}{2(2)} \\\frac{-4}{4} \\-1$

Substitute,

$2x^{2}+4x-30\\2(-1)^{2}+4(-1)-30\\2-4-30\\-32$

So the vertex is (-1,-32)

8 0

3 years ago

This parabola has<br> x-intercepts

slega [8]

Answer:

see the explanation

Step-by-step explanation:

we have the quadratic equation

$y=-16x^{2} +32x-10$

This is a vertical parabola open downward

The vertex is a maximum

Find the x-intercepts of the quadratic equation

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

$-16x^{2} +32x-10=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16x^{2} +32x-10=0$

so

$a=-16\\b=32\\c=-10$

substitute in the formula

$x=\frac{-32(+/-)\sqrt{32^{2}-4(-16)(-10)}} {2(-16)}$

$x=\frac{-32(+/-)\sqrt{384}} {-32}$

$x=\frac{-32(+/-)8\sqrt{6}}{-32}$

$x=\frac{-32(+)8\sqrt{6}}{-32}=\frac{32(-)8\sqrt{6}}{32}=0.39\ sec$

$x=\frac{-32(-)8\sqrt{6}}{-32}=\frac{32(+)8\sqrt{6}}{32}=1.61\ sec$

therefore

This parabola has two x-intercepts representing the times when the dolphin's height above water is zero feet

8 0

3 years ago

Read 2 more answers

Suppose each license plate in a certain state has three letters followed by three digits. The letters and and the digits , , and

exis [7]

Answer:

17576000 different possible license plates

Step-by-step explanation:

Note that in the question, repetition is allowed for both the letters and digits.

For the first letter, there are 26 choices to make. For the each of the letters, there are 26 choices for the second letter, and for each of the letters, there are another 26 choices for the third letter.

Therefore, this gives us 26x26x26 = 17576 possible pairs of letters.

For the three numbers, we have ten possibilities for the first digit, ten possibilities for the second digit, and ten possibilities for the third digit.

Therefore, this gives us 10x10x10 =1000 possible numbers.

The combined possibility of the license plates in both three letters and three numbers is 17576 x 1000 = 17576000 different possible license plates.

7 0

3 years ago

Triple the sum of 24 and 9

inessss [21]

so you would multiply 3 by the sum of 24 and 9...

3(24+9)=3(33)=99

4 0

4 years ago

5.62 x 10^2 in standard notation ??

Lyrx [107]

The answer is five hundred sixty.

6 0

3 years ago