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10.3
Solving Quadratic Equations
10.3 – Solving Quadratic Eq.
Goals / “I can…”
Solve quadratic equations by graphing
Solve quadratic equations using square
roots
10.3 – Solving Quadratic Eq.
When you look at a parabola, there are
many important things to consider.
Vertex
Line of symmetry
y-intercept
10.3 – Solving Quadratic Eq.
But one of the MOST IMPORTANT parts
of the graph is where it crosses the xaxis or the x-intercept.
10.3 – Solving Quadratic Eq.
To find the x-intercept, we use the
quadratic equation.
2
ax + bx + c = 0
When you solve this equation, you will
see 0, 1, or 2 solutions to the
equations. What do I mean by this?
10.3 – Solving Quadratic Eq.
“0” solutions
y
x
10.3 – Solving Quadratic Eq.
“1” solutions
y
x
10.3 – Solving Quadratic Eq.
“2” solutions
y
x
10.3 – Solving Quadratic Eq.
The x-intercept is also called the root
OR zeros. To find the zeros we can
graph or solve the equations.
10.3 – Solving Quadratic Eq.
y
x  7 x  10  0
2
roots
O
x
10.3 – Solving Quadratic Eq.
1 2
Solve
x = 8 algebraically.
2
Check your solution graphically.
SOLUTION
1 2
x = 8
2
CHECK
Write original equation.
x 2 = 16
Multiply each side by 2.
x= 4
Find the square root of each side.
Check these solutions using a graph.
10.3 – Solving Quadratic Eq.
CHECK
1
Check these solutions using a graph.
Write the equation in the form ax 2 + bx + c = 0
1 2
x =8
2
1 2
x –8=0
2
2
Rewrite original equation.
Subtract 8 from both sides.
Write the related function y = ax2 + bx + c.
y = 1 x2 – 8
2
10.3 – Solving Quadratic Eq.
CHECK Check these solutions using a graph.
2
Write the related function
y = ax2 + bx + c.
–4, 0
y = 1 x2 – 8
2
3
1
Sketch graph of y = x2 – 8.
2
The x-intercepts are  4, which
agrees with the algebraic solution.
4, 0
10.3 – Solving Quadratic Eq.
Solve x 2 – x = 2 graphically.
Check your solution algebraically.
SOLUTION
1
Write the equation in the form ax 2 + bx + c = 0
x2 – x = 2
x2 – x – 2 = 0
2
Write original equation.
Subtract 2 from each side.
Write the related function y = ax2 + bx + c.
y = x2 – x – 2
10.3 – Solving Quadratic Eq.
2
Write the related function y = ax2 + bx + c.
y = x2 – x – 2
3
Sketch the graph of the function
y = x2 – x – 2
From the graph, the x-intercepts
appear to be x = –1 and x = 2
– 1, 0
2, 0
10.3 – Solving Quadratic Eq.
From the graph, the x-intercepts
appear to be x = –1 and x = 2
– 1, 0
CHECK
You can check this by substitution.
Check x = –1:
Check x = 2:
x2 – x = 2
x2 – x = 2
?
?
(–1) 2 – (–1) = 2
22 – 2 = 2
1+1=2
4–2=2
2, 0
10.3 – Solving Quadratic Eq.
We can also find the zeroes by using a
special function on our calculators.
So……..synchronize your calculators!!!
10.3 – Solving Quadratic Eq.
graph
2
x –1=0
2
2x + 4 = 0
10.3 – Solving Quadratic Eq.
Solve:
2
3x + 12 = 12
10.3 – Solving Quadratic Eq.
Solve:
2
x – 25 = 0