1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
RSB [31]
2 years ago
5

Given a table of values of a quadratic function, which of the following do you absolutely need in order to find its equation? *

Mathematics
1 answer:
nadya68 [22]2 years ago
6 0

Answer:

The general form of a quadratic function is --> y = ax2 + bx + c

Since (0, -2) exists for the function, we can plug in those values:

-2 = a(0)2 + b(0) + c

-2 = 0 + 0 + c

-2 = c

So now our function so far is --> y = ax2 + bx - 2

We have two pairs of coordinates left: (-1, -8) and (3, -8).

First, plug in the first pair and simplify as much as you can:

-8 = a(-1)2 + b(-1) - 2

-8 = a - b - 2 ( add 2 to both sides )

-6 = a - b (stop here because we can't go further)

Second, plug in the second pair and simplify as much as you can:

-8 = a(3)2 + b(3) - 2

-8 = 9a + 3b - 2 ( add 2 to both sides )

-6 = 9a + 3b (stop here because we can't go further)

Now we have these two equations left:

a - b = -6

9a + 3b = -6

Now we solve for a and b using systems of equations, using one of three ways:

substitution

elimination

graphing (not my favorite, but it is doable)

Using substitution:

a - b = -6 can be rewritten as a = b - 6

plug into the second equation and solve for b

9(b - 6) + 3b = -6 (distribute the 9)

9b - 54 + 3b = -6 (combine all of the b's)

12b - 54 = -6 (add 54 to both sides)

12b = 48 (divide by 12 on both sides to isolate b)

b = 4

plug b into one of the original two equations

a - 4 = -6 (add 4 to both sides)

a = -2

The quadratic equation for this table is y = -2x2 + 4b - 2

You might be interested in
A building block is in shape of a cube with each side length of 5. what is the volume?
Alexeev081 [22]
5×5×5 = 125..... cubed
4 0
3 years ago
What is the volume of this triangular prism?
Vinvika [58]

Answer:

390

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Which is the solution for the equation y=5x+3
garri49 [273]

x =  \frac{y - 3}{5}

6 0
3 years ago
−7x−6y=2<br> 7x+4y=−6<br> solve for x and y
ikadub [295]

Answer:

\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:x=-2,\:y=2}

Step-by-step explanation:

\begin{bmatrix}-7x-6y=2\\ 7x+4y=-6\end{bmatrix}

\mathrm{Substitute\:}x=-\frac{2+6y}{7}

\begin{bmatrix}7\left(-\frac{2+6y}{7}\right)+4y=-6\end{bmatrix}

\begin{bmatrix}-2-2y=-6\end{bmatrix}

\mathrm{For\:}x=-\frac{2+6y}{7}

\mathrm{Substitute\:}y=2

x=-\frac{2+6\cdot \:2}{7}\\\\x=-2

5 0
2 years ago
Solve for the variable <br> -14 = x -7<br> -12x = 60<br> x+11 = -11<br> - x/4 = 2
Maurinko [17]
1) x= -7
2) x= -5
3) x=-22
4) x =8
Not sure about the last one tho
I tried to help :)
6 0
3 years ago
Read 2 more answers
Other questions:
  • Please help with both questions
    14·1 answer
  • Use Pythagorean theorem to find the missing side c=7, b=6a; find a and b
    9·1 answer
  • Is this a true proportion ? 1/2 = 5/10 A sometimes B Yes C none of these D no
    15·2 answers
  • If a^b=x, what is a^(b+2)?
    11·1 answer
  • A transformation involves a shape being_____, shifted or _________
    8·1 answer
  • Evaluate 18 -8(14 + 4) + 42.
    6·1 answer
  • !!!!! PLEASE HELP I'LL FOLLOW WHOEVER GETS IT RIGHT!!!!​
    10·1 answer
  • What number needs to be subtracted from both sides of the equation 40 = 25 + x in order to isolate the variable and solve for x?
    13·1 answer
  • Which of these is a unit of density?<br> km/m<br> kg/m?<br> kg/m<br> kg/m
    13·2 answers
  • I need the answer help as soon as possible
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!