Express into slope form

What are the vertex and axis of symmetry of the parabola y = x2 – 16x + 63?

jonny [76]

Answer:

A

Step-by-step explanation:

Remember that the x-value of the vertex when an equation is given in standard form can be found with the equation $\frac{-b}{2a}$ . So, we can take the coefficients from the equation and plug them in.

$\frac{-b}{2a} \\\frac{-(-16)}{2(1)}\\\\\frac{16}{2}\\\\8$

Now we know that the x-value of the vertex is 8. Next, the equation for the y-value is $c-ah^2$ , where h is the x-value of the vertex (8).

$(63)-(1)(8)^2\\63-64\\-1$

So the vertex is (8,-1).

Finally, the axis of symmetry is the x-value of the vertex, also called h.

Final answer, vertex: (8,-1) and axis of symmetry: x=8

Hope this helps!

3 0

3 years ago

Beth writes a number that shows 60 parts out of 100

dangina [55]

Answer:

60/100 orrrrrrrrrrrrrrrr 6/10

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Power Series Differential equation

KatRina [158]

The next step is to solve the recurrence, but let's back up a bit. You should have found that the ODE in terms of the power series expansion for $y$

$\displaystyle\sum_{n\ge2}\bigg((n-3)(n-2)a_n+(n+3)(n+2)a_{n+3}\bigg)x^{n+1}+2a_2+(6a_0-6a_3)x+(6a_1-12a_4)x^2=0$

which indeed gives the recurrence you found,

$a_{n+3}=-\dfrac{n-3}{n+3}a_n$

but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that $a_2=0$ , and substituting this into the recurrence, you find that $a_2=a_5=a_8=\cdots=a_{3k-1}=0$ for all $k\ge1$ .

Next, the linear term tells you that $6a_0+6a_3=0$ , or $a_3=a_0$ .

Now, if $a_0$ is the first term in the sequence, then by the recurrence you have

$a_3=a_0$
$a_6=-\dfrac{3-3}{3+3}a_3=0$
$a_9=-\dfrac{6-3}{6+3}a_6=0$

and so on, such that $a_{3k}=0$ for all $k\ge2$ .

Finally, the quadratic term gives $6a_1-12a_4=0$ , or $a_4=\dfrac12a_1$ . Then by the recurrence,

$a_4=\dfrac12a_1$
$a_7=-\dfrac{4-3}{4+3}a_4=\dfrac{(-1)^1}2\dfrac17a_1$
$a_{10}=-\dfrac{7-3}{7+3}a_7=\dfrac{(-1)^2}2\dfrac4{10\times7}a_1$
$a_{13}=-\dfrac{10-3}{10+3}a_{10}=\dfrac{(-1)^3}2\dfrac{7\times4}{13\times10\times7}a_1$

and so on, such that

$a_{3k-2}=\dfrac{a_1}2\displaystyle\prod_{i=1}^{k-2}(-1)^{2i-1}\frac{3i-2}{3i+4}$

for all $k\ge2$ .

Now, the solution was proposed to be

$y=\displaystyle\sum_{n\ge0}a_nx^n$

so the general solution would be

$y=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots$
$y=a_0(1+x^3)+a_1\left(x+\dfrac12x^4-\dfrac1{14}x^7+\cdots\right)$
$y=a_0(1+x^3)+a_1\displaystyle\left(x+\sum_{n=2}^\infty\left(\prod_{i=1}^{n-2}(-1)^{2i-1}\frac{3i-2}{3i+4}\right)x^{3n-2}\right)$

4 0

3 years ago

An ice cream store sells cones for $0.90 and sundaes for $1.65. On a day when 148 cones and sundaes total were sold, the sales w

monitta

Answer:

Select the most appropriate translation to the following question.

Do you have a book?

¿Qué hizo?

¿Tiene Ud. un libro?

¿Cómo se dice "pencil" en español?

¿Qué quiere decir "lapicero"?

Step-by-step explanation:

5 0

3 years ago

22 students is__% of 55<br> Pls show me in steps

kramer

Answer:

40%

Step-by-step explanation:

divide the students by the total

22/55 = P

P = 0.4 = 40%

8 0

3 years ago