1. Solving & Graphing
the Quadratic Equation
Created by Yvette Lee Source: mathisfun, purplemath, www.chaoticgolf.com/pptlessons/graphquadraticfcns2.ppt
2. What is quadratic equation?
The name Quadratic comes from "quad" meaning
square, because the variable gets squared (like x2)
3. Quadratic Functions
The graph of a quadratic function
is a parabola.
A parabola graph has an open
U-shape
NOTE! Make sure the parabola
doesn’t stop at the end of the
curve. It is continuous for all x-
values.
y
x
4. y
x
Line of
Symmetry
Line of Symmetry
Parabolas have a symmetric
property to them.
If we drew a line down the
middle of the parabola, we
could fold the parabola in half.
We call this line the line of
symmetry.
The line of symmetry ALWAYS
passes through the middle point
horizontally.
Or, if we graphed one side of
the parabola, we could “fold”
(or REFLECT) it over, the line
of symmetry to graph the other
side.
5. What is the Standard
Form of a Quadratic
Equation?
* a, b and c are known values. a can't be 0.
* "x" is the variable or unknown (you don't know it yet).
6. Let’s find a, b, and c in the
examples below.
In this one a=2, b=5 and c=3
Where is a?
In fact a=1, as we don't usually write "1x2"
b = -3 And where is c?
Well, c=0, so is not shown.
Oops! This one is not a quadratic equation, because
because it is missing x2 (in other
words a=0, and that means it can't be
quadratic)
7. But sometimes a quadratic equation doesn't look like that! For example:
8. How do we find solutions to
the quadratic equations?
What is solutions?
The "solutions" to the Quadratic Equation are where it is equal
to zero. There are usually 2 solutions (as shown in the graph
above).
They are also called "roots", or sometimes "zeros"
9. How to graph the quadratic equation
1. Find the Standard form of the quadratic equation.
2. Find the solutions(zeroes, roots) of the equation.
They are x-values on the x-axis
3. Find y-intercept
(c value in the standard form, or the term without variables)
Standard form x-value (roots) y-intercept
10. A trick when you see (x-a)(x-b)=0
Solve (x + 1)(x – 3) = 0
This is a quadratic, and I'm supposed to solve it. I could multiply
the left-hand side, simplify to find the coefficients, plug them into
the Quadratic Formula, and chug away to the answer.
But why would I? I mean, for heaven's sake, this is
factorable, and they've already factored it and set it equal to zero
for me. While the Quadratic Formula would give me the correct
answer, why bother with it? Instead, I'll just solve the factors:
(x + 1)(x – 3) = 0
x + 1 = 0 or x – 3 = 0
x = –1 or x = 3
The solution is x = –1, 3
* If you want to distribute the equation
and use the formula to find the roots, it
works too. This is just a easier and
quicker way to solve it.
11. Solve and graph x2+5x=-6
1. Is it the standard form?
No! I add 6 in each side to make
the right side to zero: x2+5x+6=0
2. What are the roots/zeroes/solutions?
a=1, b=5, c=6
Plug the numbers in the calculator
or use factoring (x+2)(x+3)=0
The solution is x=2, or 3
3. Find y-intercept. C=6, so y-intercept is 6.
Time to draw the graph.
Plot the roots and the y-intercept and make a symmetrical U shape
12. Solve and graph x2+4x=-4
1. Is it the standard form?
No! I add 4 in each side to make
the right side to zero: x2+4x+4=0
2. What are the roots/zeroes/solutions?
a=1, b=4, c=4
Plug the numbers in the calculator
or use factoring (x+2)(x+2)=0
The solution is x=2, or 2
3. Find y-intercept. C=4, so y-intercept is 4.
Time to draw the graph.
Plot the roots and the y-intercept and make a symmetrical U shape
Be the first to comment