NAME: ___________________________ NOTE: WRITE YOUR NAME ON ALL PAGES.
TEACHER: MADARANG
SUBJECT: ALGEBRA 1 WEEK 4 Due May 15
th
PERIOD: _______________
WEEK 4: Solving Quadratic Equations Using Square Roots and Graphing Quadratic Functions
Topic 1: Solving by Factoring (REVIEW)
Discussion: For the last two weeks, you have been exposed to factoring quadratic trinomials and solving for
the quadratic equation by factoring.
Let’s review: Solve the quadratic equations by factoring:
Example 1:
→ what is our magic
pair?
Since: (-7)(2) = -14 and -7+2 = -5, then our magic pair is -7
and 5.
→ factoring the
trinomial
(-7)(2) = -14 and -7+2 = -
5
→ making each = 0
+7 +7 -2 -2 → isolating the
variable
→ solution
Example 2:
To find the magic pair, we have to multiply 2 and -
15, so
Since 10(-3) = -30 and 10 +
-3 = 7, then our magic pair is 10 and -3. Our
equation becomes:
→ split the middle
→ grouping
→ factoring 1
→ factoring 2
and
NAME _______________________________________ PERIOD ___________________ WEEK 4
Topic 2A: Solving Quadratic Equations by Taking Square Roots
Example 3:
Solve by taking the square roots
→ given
→ add 1 on both sides of the eq
→ simplify/combine like terms
→ divide both sides by 4
→ simplify the fractions
→ get the square root
of both sides of the eq.
→ simplify the radicals
and → separate the positive
and negative values
Example 4:
Solve by taking the square roots:
→ given
→ add 2 on both sides of the eq
→ simplify
→ divide both sides by 25
→ simplify
→ get the square root
of both sides
→ simplify radicals
and
→ separate the positive
and the negative values
NAME ____________________________________________________ PERIOD: _________________
Topic 2B: Solving Quadratic Equations by Taking Square Roots in a Quantity
Example 5:
Solve by taking the square roots
→ given
→ get the square root of both sides
→ simplify the radicals
Separate the two answers +5 and -5 as two linear equations
and
→ solve for x by adding 2 to both sides of the equation for
BOTH equtions
→ simplifying by combining like terms
Example 6:
Solve by taking the square roots
→ given
→ add 1 to both sides
→ simplify by combining
like terms
→ divide by 2 on
both sides
Now you have isolated the quadratic expression.
→ get the square root
of both sides
→ simplify the radicals
and
→ separate the two answers, then solve for x.
Solve each equation by taking the square roots. SHOW ALL THE STEPS!!!
19.
20.
21.
22.
23.
24.
25.
26.
NAME ____________________________________________________ PERIOD: _________________
Topic 3: Graphing Quadratic Functions
Graph the quadratic function
STEP 1: Make the equation equal to zero and solve by
factoring:
and
These will be your x-intercepts on the graph. Write
them as ordered pairs (-4, 0) and (2, 0)
Let’s plot the x-intercepts (-4, 0) and (2,0)
STEP 2: Get the midpoint of -4 and 2 and draw a
vertical line through this point.
→ your line of symmetry is
Draw the vertical line on the graph.
STEP 3: Substitute x = -1 into the equation to find the
y-value
This becomes another point on your graph (-1, -9)
We call this your VERTEX.
Let’s plot the vertex (-1, -9) on the graph.
Step 4: Since you now have 3 points, you can now
graph your parabola. Your vertex will be your lowest
(or highest point) of your curve, but it should be
exactly in between your x-intercepts.
As you can see, your parabola is perfectly symmetrical
on both sides of your line of symmetry!
Note: This is not a U-shaped graph.
This is not a V-shaped graph.
It’s a parabola! And you graphed it with just 3
points!
(You might want to google what parabolas look like
and where you can find them.)
Let’s draw your curve now.
NAME ____________________________________________________ PERIOD: _________________
Okay, let’s do this! Graph the following quadratic functions. SHOW ALL THE STEPS!
27. Graph:
STEP 1: STEP 2:
STEP 3:
STEP 4:
28. Graph:
STEP 1: STEP 2:
STEP 3:
STEP 4:
29. Graph:
STEP 1: STEP 2:
STEP 3:
STEP 4:
30. Graph:
STEP 1: STEP 2:
STEP 3:
STEP 4:
