BASIC QUADRATIC FACTS Flashcards
(92 cards)
What is the equation of the axis of symmetry?
x = -b / 2a
What are the roots of a function? (other names?)
the zeros, the x-intercepts, the solutions, where the parabola crosses
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
f(x)= 3x - 9
What is a, b and c?
a = 0 , b = 3, c = 9
What are the zeros of a function? (other names?)
the roots, the x intercepts, the solutions, where the parabola crosses
How do you know if a parabola opens upward (smile) or down (frown)?
if “a” is pos it opens up? if a is negative, it opens down.
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
what completes the square and what is the factored form? x2 + 5x + ____
25/4 completes it
and
(x + 5/2) 2
is factored form
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
f(x)= 3x2-6x+3 What is the constant term?
3
it is the y intercept
f(x)= 2x2-6x+3
What is the coefficient of the linear term?
-6
this is also known as
“b”
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
why is it called a constant term
alone it would be a constant function with a constant y-value (height)
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
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.