Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The parabola y=x^(2) is reflected across the x-axis and then scaled vertically by a factor of 5 . What is the equation of the new parabola? y=

The parabola y=x2 y=x^{2} is reflected across the x x -axis and then scaled vertically by a factor of 55 .\newlineWhat is the equation of the new parabola?\newliney=□ y=\square

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Transformations of functionsright chevron icon

Full solution

Q. The parabola y=x2 y=x^{2} is reflected across the x x -axis and then scaled vertically by a factor of 55 .\newlineWhat is the equation of the new parabola?\newliney=□ y=\square
  1. Reflecting the parabola: Reflecting the parabola y=x2y = x^2 across the xx-axis means we need to multiply the yy-values by −1-1. This reflection changes the sign of the yy-values, turning the parabola upside down.
  2. New equation after reflection: The equation of the parabola after reflection across the x-axis is y=−x2y = -x^2.
  3. Scaling vertically by a factor: Scaling the parabola vertically by a factor of 55 means we need to multiply the yy-values by 55. This scaling stretches or compresses the parabola in the vertical direction.
  4. New equation after vertical scaling: The equation of the parabola after scaling vertically by a factor of 55 is y=5(−x2)y = 5(-x^2). We can simplify this by distributing the 55 into the parentheses.
  5. Final equation: The final equation of the new parabola is y=−5x2y = -5x^2.

More problems from Transformations of functions

Question
Find g(x)g(x), where g(x)g(x) is the reflection across the x-axis of f(x)=9∣x+2∣−4f(x)=9|x+2|-4.\newlineChoices:\newline(A)g(x)=9∣x+2∣−4]\text{}(A)g(x) = 9|x+2| - 4\text{]}\newline(B)g(x)=9∣x−2∣−4]\text{}(B)g(x) = 9|x-2| - 4\text{]}\newline(C)g(x)=−9∣x−2∣+4]\text{}(C)g(x)=-9|x-2| +4\text{]}\newline(D)g(x)=−9∣x+2∣+4]\text{(D)}g(x) = -9|x + 2| + 4\text{]}
Get tutor helpright-arrow

Posted 9 months ago

Question
What does the transformation f(x)↦f(x−4) f(x) \mapsto f(x - 4) do to the graph of f(x) f(x) ?\newlineChoices:\newline(A) translates it 4 units right\text{translates it } 4 \text{ units right}\newline(B) translates it 4 units down\text{translates it } 4 \text{ units down}\newline(C) translates it 4 units left\text{translates it } 4 \text{ units left}\newline(D) translates it 4 units up\text{translates it } 4 \text{ units up}
Get tutor helpright-arrow

Posted 9 months ago

Question
What does the transformation f(x)↦f(4x) f(x) \mapsto f(4x) do to the graph of f(x) f(x) ?\newlineChoices:\newline[A] stretches it vertically\newline[B] stretches it horizontally\newline[C]shrinks it horizontally\newline[D]shrinks it vertically
Get tutor helpright-arrow

Posted 8 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 99 units down of f(x)=10x+8f(x) = 10x + 8.\newlineChoices:\newline(A) g(x)=10x−82g(x) = 10x - 82 \newline(B) g(x)=10x+98g(x) = 10x + 98 \newline(C) g(x)=10x−1g(x) = 10x - 1\newline(D) g(x)=10x+17g(x) = 10x + 17
Get tutor helpright-arrow

Posted 9 months ago

Question
What kind of transformation converts the graph of f(x)=−3x2−4 f(x) = -3x^2 - 4 into the graph of g(x)=−3x2+6 g(x) = -3x^2 + 6 ?\newlineChoices:\newline[A]translation 10 units up \text{[A]translation 10 units up} \newline[B]translation 10 units down \text{[B]translation 10 units down} \newline[C]translation 10 units left \text{[C]translation 10 units left} \newline[D]translation 10 units right \text{[D]translation 10 units right}
Get tutor helpright-arrow

Posted 8 months ago

Question
The parabola y=x2y=x^{2} is scaled vertically by a factor of 77. What is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 10 months ago

Question
The parabola y=x2y=x^{2} is shifted down by 66 units and to the right by 55 units.\newlineWhat is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 10 months ago

Question
The parabola y=x2y=x^{2} is shifted up by 22 units and to the right by 33 units.\newlineWhat is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 8 months ago

Question
The parabola y=x2 y=x^{2} is scaled vertically by a factor of 110 \frac{1}{10} .\newlineWhat is the equation of the new parabola?\newliney= y=
Get tutor helpright-arrow

Posted 9 months ago

Question
You pick a card at random, put it back, and then pick another card at random.\newline44\newline55\newline66\newline77\newlineWhat is the probability of picking a number greater than 55 and then picking a 44 ?\newlineWrite your answer as a percentage.
Get tutor helpright-arrow

Posted 1 month ago

View all (13)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant