Question

What is the equation, in standard form, of a parabola that models the values in the table? x~ -1 0 2

Answer 1

Steps

• Standard Form Equation: f(x) = ax² + bx + c

So firstly, since (0,5) is one of our values we can plug it into the standard form equation to solve for the c variable (since 0 will cancel out the a and b variable):

$5=a*0^2+b*0+c\\5=c$

Now we know that the value of c is 5. Next, plug in (-1,12) into the standard form equation and simplify (remember to also plug in 5 for the c variable):

$12=a*(-1)^2+b*(-1)+5\\12=a-b+5\\7=a-b$

Next, plug (2,15) into the standard form equation and simplify:

$15=a*2^2+b*2+5\\15=4a+2b+5\\10=4a+2b\\5=2a+b$

Now, with our last two simplified equations we will create a system of equations:

$7=a-b\\5=2a+b$

Now, I will be using the elimination method with this system. With the system, add up the equations together and you will get:

$12=3a$

From here, we can solve for the a variable. With it, just divide both sides by 3:

$4=a$

Now that we know the value of a, plug it into either equation to solve for the b variable:

$7=4-b\\3=-b\\-3=b\\\\5=2(4)+b\\5=8+b\\-3=b$

Answer

Putting all of our obtained values together, your final answer is:

$f(x)=4x^2-3x+5$