Vocabulary
This is the highest or lowest point of a parabola.
Vertex
Identify the vertex of y = (x-2)^2 + 5.
(2, 5)
What is the standard form of a quadratic?
y = ax^2 + bx + c
Solve x^2 = 25.
x = +\-5
If a > 0, the parabola opens this direction.
Up
The graph of an Quadratic equation
A parabola
Identify the vertex of y = -3(x+1)^2 - 7.
(-1, -7)
Identify a, b, and c in y = 3x^2 - 7x + 12.
a = 3 ,b = -7, c = 12
Solve x^2 - 9 = 0.
X = +\-3
The axis of symmetry for y = (x+5)^2 - 2.
X =-5
The number in front of x^2 in a quadratic equation.
The coefficient “a”
Rewrite y = x^2 + 6x in vertex form.
y = (x+3)^2 - 9
Expand y = (x-5)^2 to standard form.
y = x^2 - 10x + 25
Solve by factoring: x^2 + 3x = 10.
X= 2 or -5
The y-intercept of y = x^2 + 4x + 3.
3
What you call the form y = a(x-h)^2 + k.
Vertex form
Rewrite y = 2x^2 - 8x + 3 in vertex form.
y = 2(x-2)^2 - 5
Expand y = -2(x+3)^2 + 1.
y = -2x^2 - 12x - 17
Solve using square roots: (x-4)^2 = 20.
X = 4+\- 20
How does the graph of y = 2x^2 compare to y = x^2?
It is narrower / vertically stretched
The domain of any quadratic function.
All real numbers
Give any quadratic where the vertex is (-4, 9)
Accept any: y = a(x+4)^2 + 9
Convert y = x^2 - 2x - 8 into factors.
(x-4)(x+2)
Solve using the quadratic formula:
2x^2 + x - 3 = 0.
X=1 or x= -3/2
Does y = -x^2 + 6x - 11 open up or down? Why?
Opens down because a = -1 (negative)