Quadratics
- Thread starter Rozalynda
- Start date
Q1 is is a straightforward question about using simultaneous equations
x + y = 6
x2 - y = 0
Addition of these two will eliminate y and give:
x2 + x - 6 = 0
This quadratic solves by factorisation to give x = 3 and x = -2
Substitute in the original equations gives both y results.
Q2
x2 - 2x - 5
re-arranges to
(x2 - 2x - 1) - 4
gives (x-2)2 = 4
and x - 1 = +2 or -2
and x= -1 and -3
This is a parabola that cuts x at - 1 and +3 and whose mid point is 1
So, sketch an upwardly open parabola cutting the x axis at these values and passing through the minimum point at x = 1 (plug this into the original equation to discover the minimum y value when x = 1.
Q3
You have been given the x,y values of three points and been told this is a parabola. You have even been give the form of the parabola.
Take point 1,0. This states that when x=-1 y=0
So
a - b + c = 0
(-2, 8)
4a -2b +c = 8
(1,2)
a + b + c = 2
And now you can solve for a, b and c!
x + y = 6
x2 - y = 0
Addition of these two will eliminate y and give:
x2 + x - 6 = 0
This quadratic solves by factorisation to give x = 3 and x = -2
Substitute in the original equations gives both y results.
Q2
x2 - 2x - 5
re-arranges to
(x2 - 2x - 1) - 4
gives (x-2)2 = 4
and x - 1 = +2 or -2
and x= -1 and -3
This is a parabola that cuts x at - 1 and +3 and whose mid point is 1
So, sketch an upwardly open parabola cutting the x axis at these values and passing through the minimum point at x = 1 (plug this into the original equation to discover the minimum y value when x = 1.
Q3
You have been given the x,y values of three points and been told this is a parabola. You have even been give the form of the parabola.
Take point 1,0. This states that when x=-1 y=0
So
a - b + c = 0
(-2, 8)
4a -2b +c = 8
(1,2)
a + b + c = 2
And now you can solve for a, b and c!
Cubist
Senior Member
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- Oct 29, 2019
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- 1,666
Did you Read this before posting? You should post one question per thread otherwise the response posts can become confusing. Also you're supposed to show what you've tried so that we know exactly where you're stuck (so that the help will be more useful to you)
@jonel it is great to have another potential helper on the forum! But please don't give away answers because this won't help the OP. We prefer to guide students to answer the problem themselves, and try to work out exactly where they are stuck so that we can help them to understand. Giving complete/ almost complete answers won't help them in the long run. Also try to spot people potentially cheating in online exams etc!
(I make some exceptions to giving away answers if the OP obviously isn't a student, for example a carpenter asking advice on how to calculate a particular shape to cut - but even then its best if they can be guided if they have enough of the math basics)