Question

The parabola y=x^2 is scaled vertically by a factor of 2/3. What is the new equation?

Answer 1

Answer:

Equation of the new parabola is $y=\frac{2}{3}x^2$

Step-by-step explanation:

The equation of the circle is $y=x^2$

Whenever we do some scaling in vertical direction then there should be change in the overall function or the y values.

If the function function f(x) is scaled vertically by a factor of k, then the translated function becomes kf(x).

Now, here the parabola y=x^2 is scaled vertically by a factor of 2/3.

Hence, k = 2/3

Therefore, equation of the new parabola is $y=\frac{2}{3}x^2$

Answer 2

A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The new equation of the parabola is y=(2/3)x².

What is the Equation of a parabola?

A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in the form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

The equation of the parabola given is y=x² which is needed to be scaled by a factor of 2/3 in the vertical direction. Now, since the parabola is scaled, therefore, the entire equation of y is needed to be multiplied by 2/3. Thus, the new equation will be,

$y = \dfrac{2}{3}x^2$

Hence, the new equation of the parabola is y=(2/3)x².

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