All categories

3 years ago

The standard form of the equation of a parabola is y = x2 - 8x + 29. What is the vertex form of the equation?

2 answers:

7 0

Y = x² - 8x + 29
y = (x² -8x +4²) + 29 -4² . . . . add and subtract the square of half the x-coefficient
y = (x -4)² + 13 . . . . . . . . . . . . simplify

The appropriate choice is
C. y = (x - 4)² + 13

Oxana [17]3 years ago

6 0

Answer:

y=(x-4)^2 + 13

Step-by-step explanation:

You might be interested in

Anna would like to purchase a new bike that costs $205. She already has $31 saved. If she saves a maximum of $12 a week, the fol

Dmitrij [34]

Answer:

It will take at least 15 weeks

Step-by-step explanation:

12w+31 ≥ 205

Subtract 31 from each side

12w+31-31 ≥ 205-31

12w ≥ 174

Divide each side by 12

12w/12 ≥ 174/12

w ≥ 14.5

Rounding up to the nearest integer

w ≥ 15

It will take at least 15 weeks

5 0

3 years ago

Read 2 more answers

A quadrilateral has vertices at A(-5,5), B(1,8), C(4,2), and D(-2,-2). Use slope to determine if the quadrilateral is a rectangl

AysviL [449]

Answer:

The quadrilateral is not a rectangle

Step-by-step explanation:

we know that

If a quadrilateral ABCD is a rectangle

then

Opposite sides are congruent and parallel and adjacent sides are perpendicular

Remember that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

A(-5,5), B(1,8), C(4,2), and D(-2,-2)

Plot the figure to better understand the problem

see the attached figure

Find the slope of the four sides and then compare

step 1

Find slope AB

A(-5,5), B(1,8)

substitute in the formula

$m=\frac{8-5}{1+5}$

$m=\frac{3}{6}$

$m_A_B=\frac{1}{2}$

step 2

Find slope BC

B(1,8), C(4,2)

substitute in the formula

$m=\frac{2-8}{4-1}$

$m=\frac{-6}{3}$

$m_B_C=-2$

step 3

Find slope CD

C(4,2), and D(-2,-2)

substitute in the formula

$m=\frac{-2-2}{-2-4}$

$m=\frac{-4}{-6}$

$m_C_D=\frac{2}{3}$

step 4

Find slope AD

A(-5,5), D(-2,-2)

substitute in the formula

$m=\frac{-2-5}{-2+5}$

$m=\frac{-7}{3}$

$m_A_D=-\frac{7}{3}$

step 5

Verify if the opposites are parallel

Remember that

If two lines are parallel, then their slopes are the same

The opposite sides are

AB and CD

BC and AD

we have

$m_A_B=\frac{1}{2}$

$m_C_D=\frac{2}{3}$

$m_A_B \neq m_C_D$

It is not necessary to continue verifying, because two of the opposite sides are not parallel

therefore

The quadrilateral is not a rectangle

4 0

3 years ago

A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow. Find the length of the line. If necess

LenKa [72]

Answer

14.4 ft~

Step-by-step explanation

A kite is flying 12 feet off the ground, therefore the height is 12 (assuming the line is tied to the ground if a person is holding the line then the height would be less)

Assuming the sun is positioned in such a way that the shadow represents a horizontal distance. Horizontal distance of shadow = 8

Use Pythagoras Theorem

Where a^2 + b^2 = c^2

8^2 + 12^2 = 208

Square root 208 = 14.4~

~ Hoodini, here to help :)

6 0

3 years ago

Fill in the Blank 6:15=8:_

Katen [24]

Answer:

Step-by-step explanation:

6 0

3 years ago

What is the slope of the line that passes through the points (10,5) and (9,5)? Write

Alex_Xolod [135]

Answer:

slope of line is 0.

Step-by-step explanation:

Slope of a line passing through (x1,y1) and (x2,y2) is given by

m = (y2-y1)/(x2-x1)

Given points are (10,5) and (9,5)

thus

slope = (5-5)/(9-10) = 0/-1 = 0

Thus, slope of line is 0.

When slope of line is zero it means that the line the which passes through given point is parallel to x-axis.

4 0

3 years ago