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2 years ago

A line with a slope of 3 passes through the point (0, -10). What is its equation in

1 answer:

andrey2020 [161]2 years ago

8 0

$(\stackrel{x_1}{0}~,~\stackrel{y_1}{-10})\qquad \qquad \stackrel{slope}{m}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{3}(x-\stackrel{x_1}{0}) \\\\\\ y+10=3x\implies \stackrel{\textit{slope-intercept form}}{y=3x-10}$

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Y=x^2-6x-16 in vertex form

satela [25.4K]

Answer:

$y=(x-3)^{2} -25$

Step-by-step explanation:

The standard form of a quadratic equation is $y=ax^{2} +bx+c$

The vertex form of a quadratic equation is $y=a(x-h)^{2} +k$

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

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

In this case, our quadratic equation is $y=x^{2} -6x-16$ . Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

$h=\frac{-b}{2a}$ ⇒ $h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3$

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is $y=x^{2} -6x-16$

$y=x^{2} -6x-16$ ⇒ $y=(3)^{2} -6(3)-16$ ⇒ $y=9-18-16$ ⇒ $y=-25$

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: $y=a(x-h)^{2} +k$

a: 1

h: 3

k: -25

$y=(x-3)^{2} -25$

Hope this helps!

3 0

3 years ago

IS the decimal number 5.078, the digit in the hundredths place is a 7.<br>TRUE OR FALSE?????

Ksju [112]

Answer:

TRUE

The 7 is in the hundredths place

The 0 is in the tenths place

The 8 is in the thousandths place

Step-by-step explanation:

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3 years ago

Read 2 more answers

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bulgar [2K]

Answer:

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3. I cannot read your answers in the "Why or Why Not" column in the third problem, but the answers you gave in the "Evaluate" and "Does It Work?" columns are all correct.

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3 years ago

nico put some cupcakes in the oven at 8:55 they need to bake for 25 minutes when should he take them out of the oven

victus00 [196]

Answer:

9:20

Step-by-step explanation:

25 minutes from 8:55 is 9:20

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2 years ago

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faltersainse [42]

Y=3/5x+4

this can be solved using y=mx+b where m = slope and b = y intercept

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3 years ago