CP #12 Review | Features of Graphs of Quadratic Functions

• Andre

• Noah

• Both

• Neither

Answer explanation

Neither expression is correct because the signs in both expressions are incorrect. The correct expression should be (x-5)^2-7.

• They are all identical.

• They all have the same horizontal shift, but have different vertical shifts.

• 1 has a vertical shift and 2 have a horizontal shift.

• 2 have a vertical shift and 1 has a horizontal shift.

Answer explanation

The correct choice is 2 has a vertical shift and 1 have a horizontal shift, as the graphs show different vertical and horizontal shifts among them.

• Shifts the function up 5 units.

• Shifts the function down 5 units.

• Shifts the function left 5 units.

• Shifts the function right 5 units.

Answer explanation

The -5 in y=x^2-5 shifts the function down 5 units, compared to the original y=x^2 graph.

• Shifts the function up 2 units.

• Shifts the function down 2 units.

• Shifts the function left 2 units.

• Shifts the function right 2 units.

Answer explanation

The +2 in the function shifts the graph left 2 units, as it affects the x-value by moving it horizontally.

Answer explanation

The correct equation represents the graph of y=x^2+2x-3 moved 3 units to the left by adding (x+3) to x^2 and 2x, resulting in y=(x+3)^2+2(x+3)-3.

Select all the equations with a graph whose vertex has both a positive x- and a positive y-coordinate.​

Groups:

(a) Both Positive Coordinates

,

(b) At Least 1 Coordinate is Non-Positive

Mathematical Equivalence

OFF

Mathematical Equivalence

OFF

• The coefficient is negative to represent the ball going up.

• The coefficient is negative to confuse students.

• The coefficient is negative to account for the downward acceleration due to gravity.

• The coefficient is negative to make the equation more complicated.

Answer explanation

The coefficient is negative to account for the downward acceleration due to gravity

• (3, 6)

• (0, 0)

• (6, 3)

• (3, -6)

Answer explanation

The vertex of a parabola in the form f(x) = a(x-h)^2 + k is (h, k). In this case, f(x) = -(x-3)^2 + 6, so the vertex is (3, 6).