Understanding Quadratic Functions

The video tutorial explains how to convert a quadratic function from general form to standard form. It covers the process of creating a perfect square trinomial, identifying the vertex and axis of symmetry, and graphing the parabola. The tutorial also demonstrates finding additional points for a more accurate graph and emphasizes the symmetry of the parabola.

What happens to the parabola if the coefficient 'A' in the standard form is greater than zero?

• The parabola becomes a straight line.

• The parabola opens upwards.

• The parabola does not change.

• The parabola opens downwards.

What is the first step in converting a quadratic equation to standard form?

• Multiply the equation by a constant.

• Subtract a constant from both sides.

• Isolate the x-squared and x terms.

• Add a constant to both sides.

How do you determine the constant to add when completing the square?

• Square the coefficient of x.

• Take half of the coefficient of x and square it.

• Take the square root of the coefficient of x.

• Double the coefficient of x.

What is the vertex of the parabola given by the equation y = (x + 1)^2 - 5?

• (1, 5)

• (-1, -5)

• (1, -5)

• (-1, 5)

What is the equation of the axis of symmetry for the parabola y = (x + 1)^2 - 5?

• y = 1

• x = -1

• x = 1

• y = -1

What is the y-intercept of the parabola in the original equation form?

• (0, 0)

• (0, 4)

• (0, -5)

• (0, -4)

How can you find additional points on the parabola for a more accurate graph?

• By finding the x-intercepts.

• By using only the vertex.

• By drawing random points.

• By evaluating the function at different x values.

What is the value of f(2) for the equation y = (x + 1)^2 - 5?

• 9

• -5

• -4

• 4

How can you verify the accuracy of your hand-drawn graph?

• By using graphing software.

• By checking with a calculator.

• By drawing it again.

• By asking a friend.

What is the importance of the axis of symmetry in graphing a parabola?

• It helps in finding the y-intercept.

• It is used to find the vertex.

• It divides the parabola into two symmetrical halves.

• It determines the direction of the parabola.