quadratics functions polynomials Flashcards
How do you find the x-intercepts?
Plug y as zero
How do you find the axis of symmetry?
The axis of symmetry is in between the x-intercepts.
Add the two x-intercepts and divide by two.
Can also be found by -b/2a
How do you find the coordinates of the vertex?
Method One: use the axis of symmetry as a point for x and plug in for y
a > 0
^_^ concave up
the graph cuts the x-axis twice when
discriminant greater than zero
the graph touches the x-axis if
discriminant is equal to zero
the graph misses the x-axis when
discriminant is less than zero
Definition of quadratic function
A quadratic function is a relationship between two variables x and y which can be written in the form
y=ax^2+bx+c
Where aa, bc, constants, a is not zero
a < 0
concave down
if -1 < a <1
a is not zero
the graph is wider than y = x^2
if a < -1 or a > 1
the graph is narrower than
y = x^2
general form
y = ax^2 + bx + c
completed square form
y = a (x-h)^2 + k
where is the vertex in completed square form?
h, k
What is the discriminant
-b^2 - 4(ac)
Positive definite quadratics
are quadratics which are positive for all values of x
ax^2 +bx +c > 0 for all x is Real number
A quadratic is positive definite if and only if
a > 0
discriminant < 0
Negative definite quadratics are
quadratics which are negative for all values of x.
ax^2 +bx +c < 0 for all x is Real number
A quadratic is negative definite
a < 0
discriminant < 0
factored form
f(x) = a(x-p)(x-q)
what is p and q in factored form?
the x-intercepts
If the line touches the curve, we can say that the line is __ to the curve.
If the line touches the curve, we can say that the line is tangent to the curve.
The x-coordinates of any intersection points of the graphs can be found by solving the two equations __
simultaneously
Tangent to the curve means
discriminant = 0
Quadratic inequality
can be written in either the form ax^2 + bx + c >= 0
or
ax^2+bx+c where a is not equal to zero
