Understanding Vertical Reflections and Vertex in Quadratic Relations

What happens to the graph of a quadratic relation when x² is multiplied by a negative number?

• The graph becomes a horizontal line.

• The graph reflects vertically across the x-axis.

• The graph shifts upwards.

• The graph shifts to the right.

What is the result of multiplying a quadratic equation by -1?

• The parabola shifts to the left.

• The parabola reflects across the x-axis.

• The parabola becomes wider.

• The parabola shifts upwards.

If a parabola has a negative 'a' value, what can we expect about its direction?

• It opens downwards.

• It becomes a straight line.

• It remains unchanged.

• It opens upwards.

What is the vertex of a parabola with a positive 'a' value?

• The highest point on the graph.

• The lowest point on the graph.

• The midpoint of the x-axis.

• The intersection with the y-axis.

What is the effect of a positive 'a' value on the vertex of a parabola?

• The vertex is at the origin.

• The vertex is at the minimum point.

• The vertex is undefined.

• The vertex is at the maximum point.

How can you determine if a parabola opens upwards or downwards?

• By counting the number of x-intercepts.

• By measuring the width of the parabola.

• By looking at the sign of 'a'.

• By checking if the vertex is on the x-axis.

In a quadratic equation, what does a negative 'a' value indicate about the vertex?

• The vertex is undefined.

• The vertex is at the minimum point.

• The vertex is at the maximum point.

• The vertex is at the origin.

What should you do to ensure you correctly identify the sign of 'a' in a quadratic equation?

• Subtract the x-term from both sides.

• Add a constant to both sides.

• Isolate the equation for y.

• Multiply the equation by 2.

Why is it important to rearrange a quadratic equation to isolate for y?

• To simplify the equation.

• To correctly determine the sign of 'a'.

• To eliminate the x-term.

• To find the x-intercepts.

How does the absolute value of 'a' affect the graph of a quadratic equation?

• It alters the x-intercepts.

• It affects the stretch or compression of the graph.

• It determines the direction of the parabola.

• It changes the vertex position.