quadratic function, Algebra Questions help

I have placed the questions and their answers and explanations below. Please help me understand how to solve these problems. Thank you.

Solve for m.
m2 – 14m + 24 = 0
Write your answers as integers or as proper or improper fractions in simplest form. If there are
multiple answers, separate them with commas.
m =
You answered:
m =
To factor a quadratic of the form x2 + bx + C, write it as
(x + 1)(x + 2)
where c = r1 r2 and b = r1 + 12.
Step 1: Factor.
The c term is 24, so you need to find a pair of factors with a product of 24. The b term is -14,
so you need to find a pair of factors with a sum of -14. Since the product is positive (24) and
the sum is negative (-14), you need both factors to be negative.
Make a list of the possible factor pairs with a product of 24, and then find the one with a sum of
-14.
Factor pairs of c = 24 Sum of factor pairs
-1.-24 = 24
-1 + -24 = -25
-2.-12 = 24
-2 + -12 = -14
-3.-8 = 24
-3 + -8 = -11
-4.-6 = 24
-4 + -6 = -10
The factors -2 and -12 have a sum of -14. Use those numbers to factor the quadratic inside the
parentheses, m? – 14m + 24.
m2 – 14m + 24 = 0
(m – 2)(m – 12) = 0
Step 2: Use the zero product property to solve.
According to the zero product property, if (m – 2)(m – 12) = 0, then m – 2 must be o or m –
12 must be 0. Write the two equations and solve for m.
m – 2 = 0 or
m – 12 = 0
m = 2
m = 12
The solutions are m = 2 and m = 12.
Solve using the quadratic formula.
6r2 + 6r – 5 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
ra
or r =
You answered:
r=
or r =
The quadratic formula is
-b + b2 – 4ac
2a
where a + 0. It can be used to solve a quadratic equation (ax2 + bx + c = 0).
Use the quadratic formula to solve 6r2 + + 6r – 5 = 0.
-b 02 – 4ac
2a
-662-4(6)(-5)
206)
Plug in a = 6, b = 6, and c = -5
-6 +
r
36 + 120
12
Multiply
-6 + 156
12
Add
-6 +
156
12
-6-156
or r =
Split + into + or –
12
rx 0.54 or rx -1.54
Simplify and round to the nearest hundredth
Line t includes the point (4, -8) and is parallel to line
Line s has an equation of y = -2x +
s. What is the equation of line t?
Write the equation in slope-intercept form. Write the numbers in the equation as proper
fractions, improper fractions, or integers.
You answered:
Parallel lines have the same slope.
The slope-intercept form of a linear equation is
Y = mx + b
where m is the slope and b is the y-intercept.
Step 1: Find the slope of line s.
First find the slope m of line s. This is the only time you will use the equation of line s.
y = mx + b
y = – 2x
Line s has a slope m of -2.
Step 2: Find the slope of line t.
Line t is parallel to s, so its slope is the same: -2.
Step 3: Use the slope of linet and a point on line t to find its y-intercept.
Plug the slope m = -2 and the point (4, -8) into the slope-intercept formula. Then solve for
the y-intercept b.
y = mx + b
– 8 = -2(4) + b
Plug in y = -8, m = -2, and x = 4
-8 = -8 + b
Multiply
0 = b
Add 8 to both sides
Line t has a y-intercept of 0.
Step 4: Use the slope of line t and the y-intercept of line t to find the equation of the
line.
Plug the slope m = -2 and the y-intercept b =
into the slope-intercept formula.
y = mx + b
y = -2x + 0
Plug in m -2 and bo
y = -2x
Simplify
The equation of line t in slope-intercept form is y = -2x.
Line l has equation x = -7. Find the distance between i and the point H(-3,-5).
Round your answer to the nearest tenth.
You answered:
The distance between a point and a line is the length of the segment perpendicular to the line
from the point.
The linel is a vertical line with an x-intercept of -7. The point H has an x-coordinate of – 3 and
a y-coordinate of -6.
107Y
8
6
4
4.
2
6
-10
-8
-6
-4
– 2
0
2
4
6
8
10
-2
-4
-6
H(-3,-5)
-8
– 10
Look for the point on that is directly to the left of H. This point is I(-7,-5).
2017
a
8
8
6
4
4
2
2.
-10
-8
-6
-4
-2
0
2
4
4
6
8
8
10
-2
.
-4
-6
I(-7,-6) H(-3, -6)
-8
-10
Line li has the equation y = 6 and line 12 has the equation y = -7. Find the distance between
li and 12
Round your answer to the nearest tenth.
You answered:
The distance between two parallel lines is the distance between one line and a point on the
other line.
The distance between a point and a line is the length of the segment perpendicular to the line
from the point.
The line li is a horizontal line with a y-intercept of 6. The line 12 is a horizontal line with a
y-intercept of – 7. Since 11 and 12 are both horizontal lines with different y-intercepts, they are
parallel.
To find the distance between 11 and 12, pick a point on one of the lines and find the distance
from that point to the other line. For convenience, pick the y-intercept of l1, (0,5). Call this
point Y.
10
8
8
Y(0, 6)
6
4
2
x
6
-10
-8
-6
-4
-2
0
2
4
6
8
8
10
-2
-4
-6
-8
-10
Now, calculate the distance between 12 and Y. The point Z(0, -7) lies on 12 and is directly
below Y.
101
8
8
Y(0,6)
6
4
4
2
X
6
-10
-8
-6
-4
-2
0
2
4
6
8
10
-2
.4
-6
Z(0, -7)
-8
– 10