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2 years ago

Fill in the blanks concerning the following quadratic function: f(x)=−x2−4x+5

Mathematics

1 answer:

gayaneshka [121]2 years ago

4 0

Answer:

Step-by-step explanation:

Given quadratic function is,

f(x) = -x² - 4x + 5

Leading term of the quadratic function is 'x²'

Coefficient of this leading term is (-1).

Now we will convert this standard equation into vertex form,

f(x) = -x² - 4x + 5

= -(x² + 4x) + 5

= -[x² + 2(2x) + 4 - 4] + 5

= -[x² + 2(2x) + 2²] + 4 + 5

= -(x + 2)²+ 9

f(x) = -(x + 2)² + 9

Since, coefficient of the leading term is negative the parabola will open downwards.

Vertex form of the function is given by,

g(x) = -(x - h)² + k

(h, k) is the vertex.

By comparing the equation of the function 'g' with the function 'f',

(-2, 9) will be the vertex of the function which is the maximum point of the function.

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Use undetermined coefficients to find the particular solution to 7t + 5=y''+y'-4y У, (t) - Preview Get help: Video Points possib

lions [1.4K]

Suppose $y_p=a_0+a_1t$ is a solution to the ODE. Then ${y_p}'=a_1$ and ${y_p}''=0$ , and substituting these into the ODE gives

$a_1-4(a_0+a_1t)=7t+5\implies\begin{cases}-4a_1=7\\-4a_0+a_1=5\end{cases}\implies a_0=-\dfrac{27}{16},a_1=-\dfrac74$

Then the particular solution to the ODE is

$y_p=-\dfrac{27}{16}-\dfrac74t$

5 0

2 years ago

In two or three sentences explain how you would solve for the real solutions of the following equation: please help asap!!

g100num [7]

the real solutions for the equation $x^{3}=-64$ are -

$x=4,2+-2\sqrt{3i}$

Step-by-step explanation:

$x^{3}$ = $- 64$

$x^{3} +64$ = 0

We can write 64 as $4^{3}$

$x^{3}$ + $4^{3}$ = 0

using the identity ( $x^{3}+y^{3} = (x+y)(x^{2} -xy+y^{2} )$ )

we get,

= $(x+4) (x^{2} -x*4+4^{2} )$

= $(x+4)(x^{2} -4x+16)$ ....................(1)

solving the quadratic equation ,

$x^{2} -4x+16$ =0

solutions of this quadratic equation can be obtained by

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

let use y for factors

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

$x=4x+-\sqrt{16x^{2} -64x^{2} } /2x^{2}$

$x=4+-\sqrt{16-64}/2$

$x=4+-4\sqrt{3i} /2$

<u /> $x=2+-2\sqrt{3i}$ ..................(2)

from the equation 1 we have,

$x-4=0$

which gives solution $x=4$

and from equation 2 we got $x=2+-2\sqrt{3i}$

so the real solutions for the equation $x^{3}=-64$ are -

$x=4,2+-2\sqrt{3i}$

3 0

2 years ago

Wilson frees home security system he has an 11% commission on every system he sells wislson sale for this month totaled $4264.00

Finger [1]

Wilson's commission is $469.04

Step-by-step explanation:

Given,

Commission = 11%

Total sales worth = $4264.00

Amount of commission = 11% of total sales worth

$Amount\ of\ commission=\frac{11}{100}*4264\\\\Amount\ of\ commission=\frac{46904}{100}\\\\Amount\ of\ commission=\$469.04$

Wilson's commission is $469.04

Keywords: commission, division

Learn more about division at:

#LearnwithBrainly

6 0

2 years ago

An Olympic hurdler was part of the way through her race when she fell. She got up and completed the final 353535 meters of her 1

guajiro [1.7K]

hurdler falled down before the 353535 steps of 100100100 race.

we need to find where she fell down

so we need subtract 353535 from 100100100

$100100100-353535=99746565$

she falled at 99746565 step before completing the race

5 0

2 years ago

Which type of triangle will always have a perpendicular bisector that is also an angle bisector

Fofino [41]

The answer is an equilateral triangle

5 0

2 years ago

Read 2 more answers