Formulas
What is the standard form of a quadratic equation?
ax^2+bx+c
What shape is the graph of a quadratic?
What is a parabola?
Solve: x^2 = 16
x=±4
Factor: x^2+7x+12
What is (x+3)(x+4)
True or False: All quadratics open upward.
False
What does the "b" in ax^2+bx+c
What is the coefficient of the linear term?
What is the vertex of the parabola?
What is the highest or lowest point of the parabola?
Solve using factoring: x^2+5x+6=0
x=−2 or x=−3
Factor: x^2−9
What is (x+3)(x−3)
Find the axis of symmetry for y=x^2+4x+3
x=-2
What formula is used to find the roots of a quadratic?
What is the quadratic formula: x=−b±√b2−4ac/2
How can you tell if the parabola opens up or down?
by checking the sign of a (Up if a>0, down if a<0)
Solve using the quadratic formula: x^2−3x−10=0
x=5 or x=−2
Factor: 2x^2+5x+3
What is (2x+3)(x+1)
What is the discriminant and what does it tell us?
The discriminant is b^2−4ac; it tells the number and type of solutions (real or complex, and how many).
What is the formula for the axis of symmetry of a quadratic equation?
-b/2a
What does the direction of the parabola tell you about the vertex?
whether it’s a maximum or minimum
Solve using factoring: x^2−x−12=0
x=−3 or x=4x
Factor 3x^2-12
What is 3(x + 2)(x - 2)
How many solutions does the equation x^2+6x+9=0 have, and why?
one solution, because the discriminant is 0
What is the vertex form of a quadratic?
what is y=a(x−h)^2+k?
Describe how to graph y=(x−2)^2−3
shift right 2 units and down 3 units from the origin
Solve: 2x^2+3x−2=0
x=1/2, x=−2
Factor: x^2−2x−35
What is (x−7)(x+5)
Give an example of a quadratic equation with no real roots.
x^2+4=0 – No real roots because the discriminant is negative.