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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 system is
i)
ii)
The solutions to this system, are all points (x, y) for which BOTH these 2 inequalities hold.
Check the points separately:
(5, 1)
i)
True
ii)
Not True
(0, 0)
i)
True
ii)
True
(-2, -3)
i)
True
ii)
True
(2, 5)
i)
Not True
ii)
Not True
Answer: (0, 0) and (-2, -3)
i)
ii)
The solutions to this system, are all points (x, y) for which BOTH these 2 inequalities hold.
Check the points separately:
(5, 1)
i)
ii)
(0, 0)
i)
ii)
(-2, -3)
i)
ii)
(2, 5)
i)
ii)
Answer: (0, 0) and (-2, -3)