Effects of Coefficients on Parabolas

The video tutorial explains how vertical stretches affect the shape of parabolas. It covers the impact of negative coefficients, which create downward-opening parabolas, and positive coefficients less than one, which result in wider parabolas. The tutorial demonstrates these concepts with examples, showing how coefficients change the graph's appearance.

What is the purpose of adding a coefficient in front of x^2 in a parabola equation?

• To change the vertex of the parabola

• To apply a vertical stretch or compression

• To change the direction of the parabola

• To shift the parabola horizontally

What does the negative sign in the function G(x) = -3x^2 indicate?

• The parabola opens upwards

• The parabola is wider

• The parabola opens downwards

• The parabola is shifted to the right

How does the factor of 3 affect the parabola in G(x) = -3x^2?

• It shifts the parabola downwards

• It makes the parabola wider

• It shifts the parabola upwards

• It makes the parabola narrower

What is the visual effect of multiplying x^2 by a large number?

• The parabola becomes narrower

• The parabola becomes wider

• The parabola shifts to the left

• The parabola shifts to the right

In the function G(x) = 1/3 * x^2, what does the coefficient 1/3 do to the parabola?

• It makes the parabola narrower

• It makes the parabola open downwards

• It shifts the parabola upwards

• It makes the parabola wider

What happens to the height of the parabola when multiplied by a number less than one?

• The height decreases

• The height increases

• The height remains the same

• The parabola shifts to the right

How does a positive coefficient less than one affect the parabola's width?

• It shifts the parabola upwards

• It shifts the parabola downwards

• It makes the parabola wider

• It makes the parabola narrower