Quadratic graphs
The graph of an equation with x^2 in it is a smooth U-shaped curve called a parabola.
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Analogy
Like the path of a ball thrown into the air and falling back down.
Example
Crosses x-axis at x = 1 and x = 3Turning point at x = 2: y = 4 - 8 + 3 = -1Lowest point is (2, -1)
In practice
Bridge arches, satellite dishes and the arc of a basketball shot are all quadratic shapes.
Practice
Flashcards
- What shape is the graph of y = x^2 - 4x + 3?A U-shaped curve (parabola) with its lowest point at (2, -1).
Interview questions
- Describe the graph of y = x^2 - 4x + 3 and give its turning point.
- It is a U-shaped parabola
- It crosses the x-axis at x = 1 and x = 3
- The turning point is halfway, at x = 2
- y = -1 there, so it is (2, -1)
Questions people ask
What is the turning point of a quadratic graph?
The turning point is where the curve changes direction. It is the lowest point of a U-shape or the highest point of an upside-down U. It lies halfway between the two places where the curve crosses the x-axis, if it does.
What decides if the parabola is a U or an upside-down U?
The sign of the x^2 term. A positive x^2, as in y = x^2 - 4x + 3, gives a U shape that opens upwards. A negative x^2, as in y = -x^2 + 4, gives an upside-down U that opens downwards.