What is the answer to x-2=7

Y=x^2-6x+3 help write the vertex form of the equation

Artist 52 [7]

Answer:

$y=(x-3)^2-6$

Step-by-step explanation:

$y=x^2-6x+3$

This is written in the standard form of a quadratic function:

$y=ax^2+bx+c$

where:

ax² → quadratic term
bx → linear term
c → constant

You need to convert this to vertex form:

$y=a(x-h)^2+k$

where:

(h,k) → vertex

To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:

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

Using your original equation, identify the a, b, and c terms:

$a=1\\\\b=-6\\\\c=3$

Insert the known values into the equation:

$x=-\frac{(-6)}{2(1)}$

Simplify. Two negatives make a positive:

$x=\frac{6}{2} =3$

X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:

$y=3^2-6(3)+3$

Simplify using PEMDAS:

$y=9-18+3\\\\y=-9+3\\\\y=-6$

The value of y is -6 (3,-6). Insert these values into the vertex form:

$(3_{h},-6_{k})\\\\y=a(x-3)^2+(-6)$

Insert the value of a and simplify:

$y=(x-3)^2-6$

:Done

6 0

2 years ago

Please help would mean a lot

sammy [17]

Answer:

C maybe.........

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Select the correct answer.

ivolga24 [154]

I think the answer is c

3 0

1 year ago

Read 2 more answers

Find the value of m. (-3/4)-⁴×(-3/4)-¹¹ = (-3/4)^m

tatiyna

Answer:

m = - 15

Step-by-step explanation:

Using the rule of exponents

$a^{m}$ × $a^{n}$ = $a^{(m+n)}$ , then

$(-\frac{3}{4}) ^{-4}$ × $(-\frac{3}{4}) ^{-11}$ = $(-\frac{3}{4}) ^{m}$ , that is

$(-\frac{3}{4}) ^{(-4-11)}$ = $(-\frac{3}{4}) ^{m}$

$(-\frac{3}{4}) ^{-15}$ = $(-\frac{3}{4}) ^{m}$

Equating exponents gives

m = - 15

4 0

3 years ago

Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC

Marysya12 [62]

BC is 10 units and AC is $5+5\sqrt{3}$ units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}$
AB is opposite to ∠C
BC is opposite to ∠A
AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∵ AB = $5\sqrt{2}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}$

- By using cross multiplication

∴ (BC) × sin(30) = $5\sqrt{2}$ × sin(45)

∵ sin(30) = 0.5 and sin(45) = $\frac{1}{\sqrt{2}}$

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ $\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}$

- By using cross multiplication

∴ (AC) × sin(30) = $5\sqrt{2}$ × sin(105)

∵ sin(105) = $\frac{\sqrt{6}+\sqrt{2}}{4}$

∴ 0.5 (AC) = $\frac{5+5\sqrt{3}}{2}$

- Divide both sides by 0.5

∴ AC = $5+5\sqrt{3}$ units

BC is 10 units and AC is $5+5\sqrt{3}$ units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0

3 years ago