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Solve Quadratics with a Linear and Quadratic Graph
You sometimes get a question that asks you to draw a suitable line on a graph in order to solve an equation.
You will not get marks if you use the quadratic formula (or other method) to solve the equation directly. You must draw a line on the graph.
Think about a different problem.
Think about how we would find the points of intersection for a straight line and a quadratic.
We could draw both of these lines on a grid and look for the points of intersection.
We could also solve it algebraically using simultaneous equations.
We now have a quadratic to solve. We can solve it by factorising, completing the square or using the quadratic formula.
The solution of the quadratic tells us where the two lines meet.
Now imagine you want to set a difficult question for your friend.
You decide to make them draw the two lines.
So you tell them the equation of the first quadratic that we looked at ( ) but instead of telling them the equation of the straight line, you tell them the quadratic that we solved at the end ( ). They now have to find the equation of the straight line and then draw it on the first quadratic.
Where the two lines meet tells us the solution of the quadratic.
They know that setting the first quadratic equal to a straight line will lead us to the quadratic.
By comparing this to the quadratic that you’ve asked them to solve, they can work out what the values of m and c are.
The straight line they have to draw is .
When they draw the straight line and they curve they find that the two lines meet at .
These are the solutions to the quadratic .
Another Look At Our Question
We need to work out which straight line to draw.
We know that setting the first quadratic equal to a straight line will lead us to the quadratic.
By comparing this to the quadratic that we’ve been asked to solve, we can work out what the values of m and c are.
The solutions (from the graph) are .
(If you try to solve the equation by using the quadratic formula then you can check that your answers are right, which, in this case, they are.)
It wouldn't include the pictures on this website unfortunately but i am hoping you guys could get the jist of it? Very confused with the pictures and the notes, don't know if it is anymore confusing without them?