BASIC QUADRATIC FACTS COPY COPY Flashcards
Projectile motion:
How do you find at what time it is at its peak?
h(t)= -16t2 + 44t + 95
the time at the peak is
t=-b/2a
plug in b and a to find t
If there is no constant term, what is an easy way to factor?
just factor out the x
and set the factors to zero (one solution is zero)
What is the zero product property?
(this)(that)=0
is true when
(this)=0 and when (that)=0
This is why we set factors = 0 when we solve quadratics.
f(x)= 3x2-4x+5 What is a, b and c ?
a = 3, b = -4, c = 5
How do you solve by isolating the x2 ?
When there is no linear term (no x term), simply act like you’re solving for x, but solve for x2 and in the last step, take square root of both sides ( + / - )
f(x) = ax2 + bx + c
What is the quadratic term?
ax2
thinking of the quadratic formula, why are there 2 real roots when the discriminant is positive?
with the square root of a positive, you will have to +- that in the top, giving 2 different real solutions.
Explain what a parabola with one real root (real zeros) looks like.
just touches x axis at one spot, the root (the zero), it doesn’t cross it, it bounces off it
what completes the square and what is the factored form? x2 + 5x + ____
25/4 completes it
and
(x + 5/2) 2
is factored form
what is the quadratic term’s exponent on the x ?
2
Projectile motion:
If you are answering a “when” question, what are you substituting in for?
you will substitute in for h(t) and then solve for the t
Describe what an axis of symmetry is?
it is where the parabola can fold onto itself
Does “a” have to be equal to 1 when doing quadratic formula?
NO
Explain what a parabola with two real roots (real zeros) looks like.
crosses x axis at those roots, at those x values
Does “a” have to be equal to 1 when completing a square?
YES
why is it called a constant term
alone it would be a constant function with a constant y-value (height)
What are solutions to
(x+8)(x-3) = 0
x = { -8, 3}
this is not a point on the graph, it is a set of two numbers, or two x values.
What do we call b2-4ac
discriminant
If the discriminant is positive, how many times does the parabola hit the x axis?
2
When can you just isolate the x2 and root both sides?
when there are no linear terms (only quad and const)
what is difference between (3, -2) and {3, -2}
the first is a point on a plane (over 3, down 2). The second is a set containing two values, 3 and -2, not a point.
If the discriminant is zero, what do you know about roots?
there is
one real double root
f(x)= -4x2 + 8
What is a, b and c ?
a = -4, b = 0, c = 8
What does the discriminant tell us about?
about the roots
whether they are real or not
Projectile motion: How do you find the time when it is 10 ft high?
h(t)= -16t2 + 48t +350
put 10 where h(t) is. Solve quadratic for t
Why is it called a “quadratic?”
From the latin “quadrus” which means “square”
h(t)= -16t2 + 55t - 60
what is the “-16”
that is the pull of gravity, actually, half of gravity. Gravity pulls at 32ft/sec2 at sea level.
what completes the square and what is the factored form? x2 + 6x + ____
9 completes it and (x+3)2
How do you solve by completing the square?
get all stuff on one side. Make sure a=1, take half of b and square it, add to both sides.
f(x)= 3x2-6x+5
What is the coefficient of the constant term?
5
this is also known as
“c”
What are the five ways to solve a quadratic?
isolate x2, factor, complete square, quadratic formula, graph and look for x-intercepts
What are the x intercepts of a function? (other names?)
the roots, the zeros, the solutions
how would you solve
(3x-2)(x-5)=0
(what are solutions?)
set factors = 0 and solve:
3x-2=0 and solve x-5=0
zero product property solutions x = { 5, 2/3}
what is the constant term’s exponent on the x?
0
Projectile motion:
If you are answering a “what height” question what are you solving for?
h(t).
You are trying to find a height so you plug in a t
h(t)= -16t2 + 77t +45 what is the initial velocity?
77 ft/sec