Parabola — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
The U-shaped graph of a quadratic function.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Function — A rule pairing each input with exactly one output.
What uses it later
This idea is needed for:
- Eccentricity — How far a conic is from being a circle. Zero is a circle; one is a parabola.
Practise this idea
14 questions in the course bank use Parabola, in What Is a Function?, Graphing Quadratics, Solving Quadratic Equations, Absolute Value, Piecewise & Step Functions, Parent Functions & Transformations, Polar Coordinates. The first 8 are below; the rest are in those units.
Problem 1
Which graph fails the vertical line test?
- A circle
- A straight line with slope 2
- A parabola opening up
- A horizontal line
Worked answer
A circle
A circle is crossed twice by most vertical lines
So one x gives two y values
It is not a function
Problem 2
The roots of a parabola are -1 and 7. Find the axis of symmetry.
Worked answer
x = 3
-1 + 72 = 3
x = 3
Problem 3
Which parabola is narrowest?
- y = 5x2
- y = x2
- y = 0.5x2
- y = 0.1x2
Worked answer
y = 5x2
|5| is the largest
So y = 5x2 rises fastest and is narrowest
Problem 4
A parabola has vertex (2, -3) and passes through (5, 6). Find another point on it.
Worked answer
(-1, 6)
(5, 6) is 3 right of the axis x = 2
So 3 left is x = -1
(-1, 6)
Problem 5
How many real solutions does x2 + 2x + 5 = 0 have?
Worked answer
none
4 - 20 = -16
Negative, so no real solutions
The parabola misses the x-axis
Problem 6
The graph of y = -|x| + 2 has a vertex at (0, 2) and
- opens downward
- opens upward
- is a straight line
- is a parabola
Worked answer
opens downward
-|x| turns the V upside down
So (0, 2) is a maximum
Problem 7
A parabola has vertex (-1,4) and opens upward, same width as y=x2. Write its equation.
Worked answer
y=(x+1)^2+4
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Problem 8
What is the graph of θ = 45°?
- A line through the origin
- A circle
- A ray of length 45
- A parabola
Worked answer
A line through the origin
Every distance in that one direction, including negative r backwards