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Maru [420]
3 years ago
13

What is the maximum or minimum value of the function? What is the range? y = -2x^2 + 32x - 12

Mathematics
1 answer:
alexira [117]3 years ago
5 0
Y= -2x² + 32x -12
Take the derivative, and set it equal to zero. We are finding where the slope equals zero (the peak of the parabola)
y'= -4x + 32
0 = -4x + 32
4x=32
x=8
The maximum is at the point x=8. Plugging into the original equation:
y= -2x² + 32x -12
y= -2(8)² + 32(8) -12
y= 116

The maximum is at point y=116
Keep in mind what maximum means. It is the largest value for y that the function has. That means that the range, or all possible y-values, is 
y ≤ 116.

Therefore, the answer is A) Max: 116, range: y ≤ 116
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The vertex of a parabola is the maximum or minimum value, and it’s represented by (x,y). The axis of symmetry is the vertical line that runs through the x axis, and also runs through the vertex. This means that the x value in the vertex (x,y) can represent the axis of symmetry.
8 0
3 years ago
Write the equation of the line that passes through the points (-6,-1) and (-4,2). Put your answer in fully simplified point-slop
Archy [21]

(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{2 +1}{-4 +6} \implies \cfrac{ 3 }{ 2 }

\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}{(-1)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +1= \cfrac{3}{2} (x +6) \end{array}}

4 0
1 year ago
Find the quotient .........
Nady [450]
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8 0
3 years ago
Read 2 more answers
Multiply each equation by a constant that would help to eliminate the y terms. 2x-5y=-21 3x-3y=-18 What are the resulting equati
anyanavicka [17]

Answer:

6x - 15y = -63

15x -15y = -90

Step-by-step explanation:

We need to multiply the two equations by a constant that will eliminate the y terms.

The two equations are:

2x - 5y = -21

3x - 3y = -18

Let us multiply the first by 3 and the second by 6. The resulting equations will be:

6x - 15y = -63

15x -15y = -90

Note: To solve the system of equations we can simply subtract the first from the second.

8 0
3 years ago
4x + 5y = 3<br>kx + 15y = 9 find k<br>​
9966 [12]

Answer:

12

Step-by-step explanation:

4x + 5y = 3 ................ (i)

kx + 15y = 9................(ii)

Dividing eqn (ii) by 3, we get,

k/3 x + 5y = 3.............(iii)

Subtracting eqn (iii) by eqn (i), we get,

-4x - k/3 x = 0

or, -(4 - k/3 )x = 0

or, 4 - k/3 = 0/x

or, 4 - k/3 = 0

or, 4 = k/3

or, k = 4*3

:. k = 12 (Ans)

6 0
3 years ago
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