Exploring Quadratic Functions: Problem Solving Techniques

What is the primary characteristic of the parabola we are seeking?

• It has two distinct x-intercepts.

• It opens downwards.

• Its vertex lies on the x-axis.

• Its vertex lies on the y-axis.

What is the significance of a parabola's vertex?

• It determines the parabola's width.

• It is where the parabola intersects the y-axis.

• It is the highest or lowest point.

• It indicates the number of x-intercepts.

Why does the first quadratic equation not represent the desired parabola?

• It has no real solutions.

• It opens downwards.

• Its vertex touches the y-axis.

• Its vertex is above the x-axis.

What does it mean if a quadratic equation has no x-intercepts?

• There are no real solutions.

• The parabola opens downwards.

• It intersects the y-axis twice.

• The vertex lies on the x-axis.

What makes the second quadratic equation the correct choice?

• Its vertex is at the origin.

• It has two x-intercepts.

• Its vertex lies on the x-axis.

• It opens downwards.

What is the y-intercept of the third quadratic equation?

• 3

• -3

• 0

• 2

Which equation correctly represents a parabola with its vertex on the x-axis?

• y = x^2 - 3

• y = 3x^2 + 2

• y = 2(x - 3)^2

• y = 2x^2 - 3

How many real solutions does the fourth quadratic equation have?

• None

• One

• Two

• Infinite

Which term indicates the direction in which a parabola opens?

• The C value

• The A value

• The B value

• The vertex

What is the y-intercept of the fourth quadratic equation?

• 2

• 0

• 3

• -2