2017. Category 4: Quadratic Functions and Equations

The graph of f(x) = x² was transformed to create the graph of g(x) = (x - 7.5)². Which of these describes this transformation?

• A horizontal shift to the right 7.5 units

• A horizontal shift to the left 7.5 units

• A vertical shift down 56.25 units

• A vertical shift up 56.25 units

The total number of seats in an auditorium is modeled by f(x) = 2x² - 6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?

• 32

• 13

• 20

• 16

The graph of a quadratic function is shown on the grid.

Which function is best represented by this graph?

• f(x) = x² + 3x - 4

• f(x) = -x² - 3x + 4

• f(x) = x² - 3x - 4

• f(x) = -x² + 3x + 4

The graph of quadratic function f is shown on the grid.

What is the y-intercept of the graph of f?

The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x). Which graph best represents f and h?

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What is the domain of f(x) = 9 - x²?

• f(x) ≥ 9

• All real numbers

• -3 ≤ x ≤ 3

• x ≤ 9

What is the positive solution to the equation

 $0=\frac{1}{3}x^2-3$  ?

A projectile is launched into the air from the ground. The table shows the height of the projectile, h(t), at different times.

Based on the table, which function can best be used to model this situation?

• $h\left(t\right)=99t^2+858$

• $h\left(t\right)=-4.9t^2+295t+0.6$

• $h\left(t\right)=-4.9t^2+295t+2$

• $h\left(t\right)=99t^2+1,470.3$

Which quadratic function in vertex form can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10)?

• $y=\frac{3}{4}\left(x+3\right)^2+7$

• $y=-\frac{3}{4}\left(x+3\right)^2-7$

• $y=\frac{3}{4}\left(x-3\right)^2+7$

• $y=-\frac{3}{4}\left(x-3\right)^2-7$

The graph of a quadratic function is shown on the grid.

Which equation best represents the axis of symmetry?

• y = 6

• x = 2

• y = 4

• x = 0