Understanding Parabolas and Graphs

The video tutorial reviews key concepts for an upcoming test, focusing on graph characteristics such as the axis of symmetry, vertex, roots, domain, and range. It covers graph matching, transformations, and describes how to analyze and graph equations using vertex and a-value. The tutorial also explains how to calculate the vertex and maximum/minimum from standard form equations, and provides strategies for graphing and problem-solving.

What is the axis of symmetry for the given parabola?

• y = 2

• y = -2

• x = 2

• x = -2

Which of the following represents a vertical shift of the parent function by 6 units up?

• y = (x - 6)^2

• y = x^2 + 6

• y = x^2 - 6

• y = (x + 6)^2

How does a negative a-value affect the graph of a quadratic function?

• It flips the graph upside down

• It makes the graph wider

• It shifts the graph upwards

• It shifts the graph to the right

What is the vertex of the quadratic function with a = 1, b = -7, and c = 4?

• (-1, -4)

• (-7, 4)

• (1, 4)

• (7, 4)

What is the y-intercept of the quadratic function in standard form with c = -5?

• (-5, 0)

• (5, 0)

• (0, 5)

• (0, -5)

How do you find the axis of symmetry for a quadratic equation in standard form?

• y = b/2a

• y = -b/2a

• x = b/2a

• x = -b/2a

What is the maximum value of the parabola with vertex at (-1, -4)?

• -4

• 4

• 1

• -1

Which graph has a y-intercept of positive 3?

• Graph D

• Graph B

• Graph C

• Graph A

What is the axis of symmetry for a graph with a vertex at (-1, -5)?

• x = -1

• x = 1

• y = -5

• y = 5

If a quadratic function has a vertex at (-1, -5) and a y-intercept at -2, what is another point on the graph?

• (-1, -7)

• (1, 7)

• (-1, 7)

• (1, -7)