Graphing Quadratic Functions: Vertex and Standard Form Insights

What is the shape of the graph of a quadratic function with a positive coefficient for x²?

• A straight line

• A circle

• A parabola opening downwards

• A parabola opening upwards

In the vertex form of a quadratic function, y = a(x-h)² + k, what do h and k represent?

• The axis of symmetry

• The y-intercepts

• The x-intercepts

• The coordinates of the vertex

How do you determine the next point on the graph of a quadratic function after finding the vertex?

• Use the x-intercept

• Use the y-intercept

• Travel one unit to the right and up one unit

• Travel one unit to the left and down one unit

What is the axis of symmetry for the quadratic function y = (x-1)²?

• x = 0

• x = 1

• y = 0

• y = 1

In the standard form of a quadratic function, y = ax² + bx + c, how do you find the x-coordinate of the vertex?

• x = -b/2a

• x = b/2a

• x = a/2b

• x = -a/2b

What is the y-intercept of the quadratic function y = x² + 2x - 8?

• 8

• 2

• -8

• 0

How long does it take for a ball thrown upward at 16 m/s from a 32-meter high cliff to reach its maximum height?

• 4.63 seconds

• 1.63 seconds

• 2.63 seconds

• 3.63 seconds

What is the maximum height reached by the ball thrown from a 32-meter high cliff?

• 50 meters

• 16 meters

• 45.06 meters

• 32 meters

How do you find the value of 'a' in the vertex form of a quadratic equation if you know the vertex and another point?

• By solving the equation for 'a' using the vertex

• By using the x-intercept

• By using the y-intercept

• By substituting the coordinates of the point into the equation and solving for 'a'

What is the standard form of the quadratic equation y = (x-1)² - 5?

• y = x² - 2x - 4

• y = x² - 2x - 5

• y = x² - 2x + 4

• y = x² - 2x + 5