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Neko [114]
3 years ago
8

What is the y-value if the vertex of 4x^2 + 8x - 8

Mathematics
2 answers:
Levart [38]3 years ago
6 0

The x-value is -b/(2a) = -8/(2·4) = -1.

The corresponding y-value is ...

... 4(-1)² +8(-1) -8 = 4 -8 -8 = -12

The y-value of the vertex is -12.

djverab [1.8K]3 years ago
5 0

Answer:

The y-value of the vertex is -12

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

f(x)=a(x-h)^{2}+k

where

(h,k) is the vertex of the parabola

In this problem we have

f(x)=4x^{2}+8x-8 -----> this a vertical parabola open upward

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)+8=4x^{2}+8x

Factor the leading coefficient

f(x)+8=4(x^{2}+2x)

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)+8+4=4(x^{2}+2x+1)

f(x)+12=4(x^{2}+2x+1)

Rewrite as perfect squares

f(x)+12=4(x+1)^{2}

f(x)=4(x+1)^{2}-12

The vertex is the point (-1,-12)

The y-value of the vertex is -12


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FromTheMoon [43]

Answer:

yards of carpet you need: 4*10/3=40/3=13.3333 yd^2

Step-by-step explanation:

convert feet to yard:

1 yard=3 feet so

12 feet=4 yards

10 feet=10/3 yard=3.33333 yard

yards of carpet you need: 4*10/3=40/3=13.3333 yd^2

3 0
3 years ago
Nina worked 32 hours this week. She earned a total of 360. How much does she make per hour? Write and solve equation.
NeX [460]

Nina makes 11.25 per hour.

Step-by-step explanation:

Given,

Number of hours worked by Nina = 32 hours

Amount earned by Nina = 360

Let,

x represent the amount earned by Nina per hour.

Amount per hour * Number of hours = Amount earned

32*x=360\\32x=360

Dividing both sides by 32

\frac{32x}{32}=\frac{360}{32}\\x=11.25

Nina makes 11.25 per hour.

Keywords: variable, equation

Learn more about variables at:

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5 0
3 years ago
Solve the equation.<br><br> y + 6 = –3y + 26
Sergeeva-Olga [200]
     y + 6 = -3y + 26
+ 3y        + 3y 
   4y + 6 = 26
         - 6   - 6
         4y = 20
          4      4
           y = 5
3 0
3 years ago
Read 2 more answers
Decide whether the relation is a function:<br> {(-3, 7), (1, -8), (6, -6), (7-8), (12, 2)}
lakkis [162]

Answer:

It is a function

Step-by-step explanation:

A function is of the form:

\left[\begin{array}{c}x_1&x_2&x_3\\-&-&-\\x_n\end{array}\right]            \left[\begin{array}{c}y_1&y_2&y_3\\-&-&-\\y_n\end{array}\right]

Where each of the x values must be distinct.

The x values are referred to as domain while the y values are called range.

Having said that, the given data can be represented as follows:

\left[\begin{array}{c}-3&1&6\\7&12\end{array}\right] ----------- \left[\begin{array}{c}7&-8&-6\\-8&2\end{array}\right]

<em>From the representation above, none of the x values are repeated.</em>

<em>Hence, it is a function</em>

6 0
2 years ago
Determine which quadrilaterals have the properties given in the table.
svetoff [14.1K]

The two quadrilateral with the listed properties are kite and rhombus respectively.

<h3>Properties of a kite</h3>
  • It has two diagonals intersecting  at right angles
  • A kite is symmetrical about its main diagonal
  • Angles opposite to the main diagonal are equal
  • The kite can be viewed as a pair of congruent triangles with a common base
  • Its diagonals are perpendicular

<h3>Properties of a rhombus</h3>
  • All sides of the rhombus are equal
  • The opposite sides are parallel
  • Opposite angles are equal
  • Diagonals bisect each other at right angles
  • Diagonals bisect the angles
  • The sum of two adjacent angles is equal to 180 degrees, that is, are supplementary

Thus, the two quadrilateral with the listed properties are kite and rhombus respectively.

Learn more about quadrilaterals here:

brainly.com/question/16691874

#SPJ1

6 0
2 years ago
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