Download Algebra 10.3 Notes

Solve Quadratic Equations by Graphing (10.3)
Definition: A Quadratic Equation is an equation that can be written in the standard form:
ax2 + bx + c = 0
Write the equation in standard form.
Ex. x2 – 2x = 3
Ex. x2 + 5x = -7
Ex. x2 + 7 = 4x
Ex. x2 = -2x + 9
 Remember that a Solution to any equation is the number or numbers that make the
equation true.
 So the Solution for a Quadratic Equation value or values of x that will make the quadratic
function equal 0.
Determine whether the given value is a solution of the equation.
Ex. x2 + 3x – 10= 0; 5
Ex. x2 – 5x – 6 = 0; 6
Ex. x2 – 4x – 5 = 0; -5
Ex. x2 – 6x – 16 = 0; -2
 We learned that we can solve a quadratic equation by Factoring last chapter.
x2 + 6x + 5 = 0
Solutions: x = ______ and x = ______
 Now look at the graph of y = x2 + 6x + 5
Notice that the two solutions that we found
by factoring x = ________ and x = ______
are the points on the ___________ where the
parabola intersects it.
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Quadratic Equations can have a different number of solutions depending
on where the parabola is on the coordinate system.
_____ Solution(s)
______ Solution(s)
_______ Solution(s)
_____ point(s) of intersection
_____ point(s) of intersection
_____ point(s) of intersection
Use the graph to find the solution(s) of the given equation.
Ex. x2 – 5x + 4 = 0
Ex. x2 – 6x + 9 = 0
Ex. x2 + 5 = 0
Solution ____________
Solution ____________
Solution ____________
Ex. x2 – 6x – 16 = 0
Ex. -3x2 + 6 = 0
Ex. x2 + 10x + 25 = 0
Solution ____________
Solution ____________
Solution ____________
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