Download Bellwork - OnCourse

BELLWORK
• Describe the relationship between the real solutions
of 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 and the graph of 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐.
QUADRATIC EQUATIONS
REAL LIFE SITUATIONS
BLOOD PRESSURE
The graph illustrates that a
person’s normal systolic blood
pressure, measured in millimeters
of mercury (mm Hg), depends
on his or her age. (The graph
starts at 100 mm Hg). The formula
𝑃 = 0.006𝐴2 − 0.02𝐴 + 120
Models a man’s normal systolic
blood pressure P at age A.
a.) find the age, to the nearest
year, of a man whose normal
systolic blood pressure is 125 mm
Hg.
b.) use the graph to describe the
differences between the normal
systolic blood pressure of men
and women as they age.
BLOOD PRESSURE
• The formula 𝑃 = 0.01𝐴2 + 0.05𝐴 + 107 models a
women's normal systolic blood pressure, P, at age A.
Use this formula to find the age, to the nearest year,
of a women whose normal systolic blood pressure is
115 mm Hg. Use the graph to verify your solution.
THE PYTHAGOREAN THEOREM
• The sum of the squares of the lengths of the legs of
a right triangle equals the square of the length of
the hypotenuse. If the legs have the length a and b,
and the hypotenuse has length c, then
𝑎2 + 𝑏 2 = 𝑐 2
c
a
b
USING THE PYTHAGOREAN THEOREM
a.) A wheelchair ramp with the length of 122 inches
has a horizontal distance of 120 inches. What is the
ramps vertical distance.
b.) Construction laws are very specific when it comes
to access ramps for the disabled. Every vertical rise of
1 inch requires a horizontal run of 12 inches. Does this
ramp satisfy the requirement.
TELEVISION
• In a 25-inch television set, the length of the screen’s
diagonal is 25 inches. If the screen’s height is 15
inches, what is it’s width?
DOES IT MAKE SENSE?
Determine whether each statement makes sense or
does not make sense, and explain your reasoning.
2
1) Because I want to solve 25 x  169  0 fairly
quickly, I’ll use the quadratic equation.
2) I’m looking at a graph with one x-intercept, so it
must be the graph of a linear equation?
3) I obtained -17 for the discriminant, so there are
two imaginary solutions.
4) When I use the square root property to determine
the length of a right triangles side, I don’t even
bother to list the negative square root.
TRUE/FALSE
Determine if the statement is true or false. If it is false,
make the necessary changes to make it true.
2
(
2
x

3
)
 25 is equivalent to 2x  3  5
1) The equation
2) Any quadratic equation that can be solved by
completing the square can be solved by the
quadratic formula.
3) The quadratic formula is developed by applying
factoring and the zero product principle to the
quadratic equation ax 2  bx  c  0
4) In using the quadratic formula to solve the
quadratic equation 5 x 2  2 x  7 , we have a=5,
b= 2, c= -7