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Answer:
Step-by-step explanation:
The given points are (-1,0) and (3,0) to find an equation of parabola. Notice that they say or the given points are x-intercepts, which means they make it easier for us to find an equation of parabola using these x-intercepts.
Quick Note:
- x-intercepts are simply the roots or solutions of quadratic equation, so if our root is x = -2 then we can write as (-2,0) and write back to x+2=0.
So what we are going to do is to write the roots’ equation back as
Our points or roots are given, therefore:
If x = -1 then x+1=0
If x = 3 then x-3=0
Then multiply x+1 with x-3 because if (x-1)(x+3)=0 then x-1=0 or x+3=0:
Convert 0 to y since we want to find a function:
Expand the expressions in and simplify to standard form:
Therefore, the equation is
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Summary
If we are given the points and
with wideness of the graph or a-value = 1 then the parabola equation is:
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Others
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The solutions for is option 3.
Step-by-step explanation:
Step 1:
First, we must bring the equation to the form of
So becomes
The value of a is the coefficient of the term, the value of b is the coefficient of x term and c is the coefficient of the constant term.
Comparing the above equation to we get
and
We have the formula
Step 2:
By substituting the known values, we get
This is the third option.