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In this lesson, we will learn how to solve quadratic equations by graphing.

Q1:

Consider the equation π¦ = π₯ β 3 π₯ β 1 0 ο¨ .

Find the solutions when π¦ = 0 .

Find the solutions when π ( π₯ ) = β 6 .

Find the solutions when π ( π₯ ) = β 1 0 .

The solutions found can be plotted in plane as seen in the given figure. What will be true of the plot of any other solution?

Q2:

Work out the coordinates that satisfy the equation π¦ = π₯ + 4 π₯ β 5 2 for the given values of π¦ .

π¦ = 7 .

π¦ = 0 .

π¦ = β 5 .

π¦ = β 9 .

Q3:

If the graph of the quadratic function π cuts the π₯ -axis at the points ( β 3 , 0 ) and ( β 9 , 0 ) , what is the solution set of π ( π₯ ) = 0 in β ?

Q4:

The curve of a quadratic function, π , intersects the π₯ -axis at the points ( 1 , 0 ) and ( β 4 , 0 ) . What is the solution set of the equation π ( π₯ ) = 0 ?

Q5:

If the point ( 9 , 0 ) is the vertex of the graph of the quadratic function π , what is the solution set of the equation π ( π₯ ) = 0 ?

Q6:

The diagram shows the graph of π¦ = π ( π₯ ) . What is the solution set of the equation π ( π₯ ) = 0 ?

Q7:

Q8:

Consider the equation π¦ = π₯ β 5 π₯ + 3 2 . In the following, find a solution by filling the blank space.

( 2 , ) .

( β 1 , ) .

( 0 , ) .

( 4 , ) .

These solutions ( π₯ , π¦ ) can be plotted as seen in the figure. What will be true of any other solution plotted in the plane?

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