Vocabulary
The symmetrical curve of the graph of a quadratic function
What is parabola?
The axis of symmetry for f(x) = 2x2 + 8x + 8
What is the AOS of x = -2?
Use the formula x = -b/2a
The x-intercepts of the quadratic function f(x)=x2−4x+4?
What is x=2?
To find the x-intercepts, set f(x)=0 and solve for x.
The quadratic can be factored as (x−2)2=0, so the x-intercept is x=2
What is the minimum or maximum value for a quadratic function with the vertex of (4, -11)?
Minimum value of -11
The general form of a quadratic function, what is a, b and c
What is f(x)=ax2+bx+c, where a, b, and c are constants.
The term of the highest or lowest point of a quadratic function
What is vertex?
The axis of symmetry of the quadratic function: f(x)=−22+4x+5
What is the axis of symmetry x = 1?
Use the formula x = -b/2a
does the following function have a minimum or maximum value? What is the y-intercept?
f(x) = -7x2 –3x +12
max value, the y-intercept is 12
What is the vertex for the function
f(x) = 5(x-15)2 – 100?
vertex = (15, -100)
is this function quadratic? Explain.
f(x) = x (x-1) (4x+2)
no, once you expand the expression, it is a polynomial of degree three
The type of function that has the highest power of 2
What is a quadratic function?
The axis of symmetry for f(x) = x2 + 4x +3
(completing the square)
What is x = -2?
Use the formula x = -b/2a
The vertex of the quadratic function f(x)=−2x2+8x−5 is a minimum or maximum point
What is the functions' vertex at a maximum point?
To find the vertex, use x=−b/2a
a=−2 and b=8.
x = -8/2(-2) = 2
Substituting x=2 into the equation
f(2)=−2(2)2+8(2)−5 = 3.
The vertex is at (2,3), and since the coefficient of x2 is negative, it represents a maximum point.
if the vertex of a quadratic function is (-3, -1) and represents a minimum point, what is the domain and range of this function?
Domain = {x| x∈R }
Range = {y| y>-1 }
Explain the significance of the coefficient a in a quadratic function.
What is the coefficient a that determines whether the quadratic function opens upwards (a>0) or downwards (a<0).
Define the term “axis of symmetry” in the context of quadratic functions
What is a vertical line that divides a parabola into two symmetric halves and passes through the vertex of the parabola?
The axis of symmetry for the function:
y=-(x-2)2 + 1
What is x = 2?
The y-intercept of the quadratic function f(x)=3x2−12x+9.
What is the y-int y = 9?
To find the y-intercept, x=0 and solve for f(x).
So, f(0)=3(0)2−12(0)+9 = 9.
The vertex of the quadratic function f(x)=2x2−8x+6
What is the vertex of a function that is at (2,-2)?
Use formula x=-b/2a, and substitute to solve for y --> (x,y) = vertex
Discuss the relationship between a parabola's vertex and its symmetry axis.
The vertex of a parabola lies on its axis of symmetry. The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two symmetric parts.
The two names for the x intercepts on a quadratic function?
What is roots and zeros?
The axis of symmetry for f(x) = 2x2 - 4x + 1
What is x = 1?
x= -b/2a
x= -(-4)/(2(2))
= 4/4
= 1
The vertex that represents whether the min or max point of the quadratic function f(x)=2x2−4x+7
What is the quadratic function's vertex representing a min point?
To find the vertex, use x= -b/2a
a=2 and b=−4.
So, x=−(-4)/2(2)=1.
Substituting x=1 into the equation, f(1)=2(1)2−4(1)+7=5
For the quadratic function f(x)=−3x2+12x−9, find the coordinates of the vertex
What is the vertex of the function that is at (2,3)
Use formula x=-b/2a, and substitute to solve for y --> (x,y) = vertex
How can you determine whether the vertex of a quadratic function represents a maximum or minimum point without solving for it?
What is the coefficient a in a quadratic function that determines whether the vertex represents a maximum or minimum point. If a>0, the parabola opens upwards, and the vertex represents a minimum point. If a<0, the parabola opens downwards, and the vertex represents a maximum point.