Graphs of Quadratic Functions

What is the vertex of the parabola y = x² - 4x + 3?

• (0, 3)

• (3, 2)

• (1, 4)

• (2, -1)

Graph the parabola y = 2x² - 8x + 6 in standard form. Label the vertex and x-intercepts.

• The vertex of the parabola is (2, -2) and the x-intercepts are (1, 0) and (3, 0).

• The vertex of the parabola is (-1, 4) and the x-intercepts are (0, 0) and (2, 0).

• The vertex of the parabola is (0, 0) and the x-intercepts are (2, 0) and (4, 0).

• The vertex of the parabola is (3, 5) and the x-intercepts are (2, 0) and (4, 0).

Tags

CCSS.HSF-IF.C.7A

How do the coefficients 'a', 'h', and 'k' affect the graph of a parabola in the standard form y = ax² + bx + c?

• The coefficient 'a' affects the vertical shift, 'h' affects the direction, and 'k' affects the width of the parabola.

• The coefficient 'a' affects the direction, 'h' affects the vertical shift, and 'k' affects the horizontal shift of the parabola.

• The coefficient 'a' affects the direction and width, 'h' affects the horizontal shift, and 'k' affects the vertical shift of the parabola.

• The coefficient 'a' affects the horizontal shift, 'h' affects the width, and 'k' affects the vertical shift of the parabola.

A ball is thrown into the air, and its height, in meters, t seconds after it has been thrown is given by the equation y = x² - 6x + 9. Write the equation in vertex form.

• y = (x-9)^2

• y = (x+3)^2

• y = (x-3)^2

• y = (x-6)^2

A ball is thrown into the air, and its height in meters after t seconds can be modeled by the equation y = 3(t+2)² + 5. What are the coordinates of the vertex of this parabola, representing the ball's highest point?

• (-2, 5)

• (-2, 3)

• (6, 5)

• (2, 5)

A roller coaster's path can be modeled by the equation y = 2x² + 4x - 3. What is the height of the roller coaster when it crosses the vertical (y) axis?

• (0, 1)

• (0, 3)

• (0, -3)

• (0, 0)

Tags

CCSS.HSF-IF.C.7A

A civil engineer is designing a parabolic arch for a new bridge. The equation of the arch is given by y = -x² + 4x - 4. Help the engineer determine the highest point of the arch (vertex) and the points where the arch intersects the water level (x-intercepts).

• The highest point of the arch is (4, 0) and the points where it intersects the water level are (4, 0) and (4, 0)

• The highest point of the arch is (2, 0) and the points where it intersects the water level are (2, 0) and (2, 0)

• The highest point of the arch is (2, 0) and the points where it intersects the water level are (2 + √5, 0) and (2 - √5, 0).

• The highest point of the arch is (0, 2) and the points where it intersects the water level are (0, 4) and (0, -4)

What is the significance of the point (h, k) in the vertex form of a quadratic function?

• The point (h, k) represents the x-intercept of the parabola.

• The significance of the point (h, k) is that it represents the coordinates of the vertex of the parabola.

• The point (h, k) is the axis of symmetry of the parabola.

• The point (h, k) has no significance in the vertex form of a quadratic function.

Graph y = (x-3)² - 4

Tags

CCSS.HSA.CED.A.2

What is the axis of symmetry for the parabola given by the equation y = -3x² + 6x - 2?

• x = -1

• x = 1

• x = 0

• x = 2