Vocabulary
A fixed point on the interior of a parabola used in the formal definition of the curve
Focus
What is the relationship between the distance of a point on the parabola to the focus and directrix?
They are equidistant
f(x)=3
G(x)=x2-7x+10
Where is f(x)=g(x)?
x=5.79, x=1.21
Find the x intercepts.
f(x)=2x2-8
x=-2, x=2
A line perpendicular to the axis of symmetry used in the definition of a parabola
Directrix
A parabola has a focus on the origin and it's directrix is y=7. What is the equation of the parabola?
y=-1/14x2+7/2
f(x)=x2-10x+42
g(x)=9x-42
Where is f(x)=g(x)
x=12, x=7
What is the y-intercept of the function?
f(x)=x2+6x+2
What do you use the quadratic formula for?
To see where the parabola crosses the x -axis
A parabola has a focus of (2,5) and the directrix is y=2. What is the equation of the parabola in standard form?
y=1/6x2+2/3x+25/6
2y+40x-6=0
y-5x2-3=0
x=0, x=-4
Quadratic functions have two x-intercepts
Always
Sometimes
Never
Sometimes
What is the equation for the quadratic formula?
-b +/- the sq rt b2-4ac
2a
Write the equation of a parabola with a focus of (-1,-2) and a directrix y = -4.
y=1/4x2+1/2x+11/4
Find the solutions to the systems.
y=x2+2x+4
y=x2+8
(2,12)
Quadratic functions have one y-intercept
Always
Sometimes
Never
Always