Transformations
What does h control in:
f(x)=a(x-h)2+k
What are horizontal shifts left and right
What is the equation for Axis of Symmetry?
What is -b/2a
What do we call the line that is closest to going through all points in a data set?
What is Line of Best Fit?
What is the quadratic formula?
What is x=(-b+-√ (b2-4ac))/2a
When looking at the graph of a system of equations, where are the solutions?
What is where the lines intersect?
What transformations have acted upon the questions:
f(x)=-x2-2x+2
What is a reflection over x-axis and shift left 1, up 3
Without looking at a graph, does f(x)=-x2+4x-3 have a maximum or minimum?
What is a maximum?
Write an equation of the parabola Mr. Holloway will show in vertex form.
What is y=-3(x+2)2+6
Solve 2x2-11x+12=0 using the quadratic formula - Show your work
What is x=1.5 or x=4
Solve the system through substitution (Show your work):
y=-2x+4
y=3x-1
What is (1,2)
Describe the transformation of the graph then identify the vertex:
f(x)=3(x+2)2+1
What is a vertical stretch by a factor of 3, a translation 2 units left and 1 unit up; (-2,1)
What is the Axis of Symmetry and Vertex of the following equation:
f(x)=4x2-2x+8
What is AoS: 1/4;
Vertex: (1/4, 31/4)
Write an equation of the parabola Mr. Holloway will show in intercept form.
What is y=-4(x-2)(x-4)
Solve f(x)=-7x+6=-4x2
What is No Real Solution?
What must be true of two quadratic functions when the parabolas open in the same direction if they are to intersect (Besides having infinite solutions).
What is: the a values of each quadratic must be different.
Draw the graph of the equation:
f(x)=1/2(x+1)2+3
What is - Mr.Holloway will show the graph
In general, what is the ordered pair for the vertex of a function?
What is ( -b/2a , f(-b/2a) )
Do quadratic functions with the same x-intercepts have the same equations, vertex, and axis of symmetry? Explain your reasoning.
No; the vertices could have different y-coordinates and therefore different equations.
Describe and correct the error in solving the equation:
2(x+1)2+3=21
2(x+1)2=18
(x+1)2=9
x+1=3
x=2
The student did not do plus or minus 3, x=2 and x=-4
Solve the system through substitution:
5x+y=2x2+6
y+x=4x-2
What is (2,4)
Write the function given the following transformations, then identify the vertex.
f(x)=8x2-6; horizontal stretch by a factor of 2 and a translation 2 units up, followed by a reflection in the y-axis.
What is g(x)=8(1/2x)2-4;(0,-4)
Consider the graph in the form f(x)=a(x-p)(x-q). Suppose its vertex is in quadrant 1 and it opens down. It also has an x-intercept where x<0 and one where x>0.
What do we know about a, p, and q?
a is negative, and p OR q must be negative.
The table shows the numbers y (in thousands) of people in a city who regularly use sharable electric scooters x weeks after the scooters are introduced. Write a function that models the data. Use the model to predict the number of users after 32 weeks.
y=.026x2-.02x+1.6; about 27,600 users.
One student says that x2=-49 has zeroes x=7 and x=-7 on the graph. Are they correct? Justify yourself without solving for x or graphing
What is No solution. It never crosses the x-axis
Write a non-linear system that has two unique solutions with the same y-coordinate of 4. Justify by solving.
What is y=x2 and y=4? Solutions being (-2,4) and (2,4).