Standard Form
What does the “c”, in standard form, represent?
Y = Ax2 +Bx + C
Y-intercept
Which way does this parabola open?
Y=-2(x-3)2+5
Down
What are the other 2 names for the x-intercepts of a quadratic relation?
Zeros or Roots
If the roots of a quadratic are -2 and 8, and the a-value is -3, does the parabola have a maximum or minimum value?
Maximum
What are the names of the 3 forms of quadratic equations?
Standard Form
Factored Form
Vertex Form
Does y = 3x2 +5x + 1 have a maximum or a minimum?
Minimum
If the vertex is at (4,6), what is the equation of axis of symmetry?
X=4
What are the x-intercepts of
Y=-(x-4)(x+5)
{4, -5}
What are the solutions to a quadratic equation called?
Roots, zeros, or x-intercepts
How many real roots can a quadratic relation have?
Zero, one (two identical), or two distinct roots
How do I find the x-intercepts of an equation?
Let y=0, and solve for x.
Does y= -2(x-7)2 - 5 have a maximum or a minimum?
Maximum
What is the axis of symmetry for this equation?
Y=(x-5)(x+7)
X=-1
A rocket is launched from a launch pad 50 feet off the ground. The “a” value in the quadratic equation that could represent this situation would be _____tive.
Negative
The name of the line that cuts a parabola into 2 equal parts is…
Axis of Symmetry
In order to find the _________________, evaluate the equation at x=0.
Y-intercept
What is the basic “step pattern” for a quadratic relation, and where does the step start?
The (1,3,5,…) step pattern starts at the vertex.
The y-intercept of
Y=2(x+4)(x-7)
-56 or (0,-56)
If R represents revenue and n represents the number of coffees sold, when does this business break-even?
R=-2.5(n-550)(n-958)
Breakeven at {550,958} coffees
Or
550 or at 958 coffees sold
What are the x-intercepts of
Y=-3(x+2)2
-2
{-2}
Or (-2,0)
What is this quadratic in standard form?
Y + 3x - 7 = 2x2
Y=2x2 - 3x +7
How does the shape of y=3x2 compare to y=1x2
It is more narrow.
What is the vertex of
Y=2(x-5)(x+7)
(-1,72)
What is the minimum value of
Y=3(x+1)(x-7)
-48
Which Form is this quadratic in?
Y=2x(x+7)
Factored Form