What is the general form of a quadratic equation?
y = ax2 (2 is ‘to the power of 2’) + bx + c
What shape is a quadratic graph?
A parabola
What does the value of a determine?
The direction and width of the parabola
What happens if a>0?
The graph opens upwards
What happens if a<0?
The graph opens downwards
What is the vertex?
The turning point (maximum or minimum)
Formula for the x-coordinate of the vertex?
x = -b/2a
What is the axis of symmetry?
A vertical line through the vertex
Equation of the axis of symmetry?
x = -b/2a
What is the y-intercept?
Where the graph crosses the y-axis
How do you find the y-intercept?
Set x=0, answer is c
What are roots (x-intercepts)?
Points where the graph crosses the x-axis
What equation do you solve to find roots?
ax2 (2 is ‘to the power of 2’) + bx + c = 0
What formula finds the roots?
Quadratic formula
What is the discriminant?
b2 (2 is ‘to the power of 2’) − 4ac
What if the discriminant < 0?
No real roots
What does symmetry mean in quadratic graphs?
Both sides of the graph mirror each other
What if the discriminant is > 0?
Two real roots
Steps to sketch a quadratic graph?
Find vertex, axis, intercepts, then draw curve
What if the discriminant = 0?
One real root
