Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

ratic Functions- No Graphing Calculator
Name:
when necessary. You must use correct notation for full credit.
Date:
Pavlina
ey Features
the key features of the following graph.
2) y-intercep
3) Axis of Symmetry:
5) Domain:

:R
7) Increasing:
4) Vertex:
6) Range:

:R
8) Decre
Form:
asked to graph 
f(x)=-(x-2)^(2)+5 and produced the following 
g
y
a) Name at least one transformatic

ratic Functions- No Graphing Calculator\newlineName:\newlinewhen necessary. You must use correct notation for full credit.\newlineDate:\newlinePavlina\newlineey Features\newlinethe key features of the following graph.\newline22) y-intercep\newline33) Axis of Symmetry:\newline55) Domain:\newline:R : \mathbb{R} \newline77) Increasing:\newline44) Vertex:\newline66) Range:\newline:R : \mathbb{R} \newline88) Decre\newlineForm:\newlineasked to graph f(x)=(x2)2+5 f(x)=-(x-2)^{2}+5 and produced the following g g \newliney\newlinea) Name at least one transformatic

Full solution

Q. ratic Functions- No Graphing Calculator\newlineName:\newlinewhen necessary. You must use correct notation for full credit.\newlineDate:\newlinePavlina\newlineey Features\newlinethe key features of the following graph.\newline22) y-intercep\newline33) Axis of Symmetry:\newline55) Domain:\newline:R : \mathbb{R} \newline77) Increasing:\newline44) Vertex:\newline66) Range:\newline:R : \mathbb{R} \newline88) Decre\newlineForm:\newlineasked to graph f(x)=(x2)2+5 f(x)=-(x-2)^{2}+5 and produced the following g g \newliney\newlinea) Name at least one transformatic
  1. Identify y-intercept: Identify the y-intercept of the function f(x)=(x2)2+5f(x) = -(x - 2)^2 + 5.\newlineThe y-intercept occurs where x=0x = 0. Substitute x=0x = 0 into the function to find the y-intercept.\newlinef(0)=(02)2+5f(0) = -(0 - 2)^2 + 5\newlinef(0)=(2)2+5f(0) = -(-2)^2 + 5\newlinef(0)=4+5f(0) = -4 + 5\newlinef(0)=1f(0) = 1\newlineThe y-intercept is the point (0,1)(0, 1).
  2. Determine axis of symmetry: Determine the axis of symmetry for the function f(x)=(x2)2+5f(x) = -(x - 2)^2 + 5.\newlineThe axis of symmetry for a parabola in the form f(x)=a(xh)2+kf(x) = a(x - h)^2 + k is the vertical line x=hx = h. Here, h=2h = 2.\newlineThe axis of symmetry is the line x=2x = 2.
  3. Find vertex: Find the vertex of the function f(x)=(x2)2+5f(x) = -(x - 2)^2 + 5.\newlineThe vertex of a parabola in the form f(x)=a(xh)2+kf(x) = a(x - h)^2 + k is the point (h,k)(h, k). Here, h=2h = 2 and k=5k = 5.\newlineThe vertex is the point (2,5)(2, 5).
  4. Determine domain: Determine the domain of the function f(x)=(x2)2+5f(x) = -(x - 2)^2 + 5. The domain of any quadratic function is all real numbers, denoted as (,)(-\infty, \infty) or R\mathbb{R}.
  5. Determine range: Determine the range of the function f(x)=(x2)2+5f(x) = -(x - 2)^2 + 5.\newlineSince the coefficient of the squared term is negative, the parabola opens downwards. This means the maximum value of the function is at the vertex. The range is all real numbers less than or equal to the y-coordinate of the vertex.\newlineThe range is (,5](-\infty, 5].
  6. Identify intervals: Identify the intervals where the function f(x)=(x2)2+5f(x) = -(x - 2)^2 + 5 is increasing and decreasing.\newlineSince the parabola opens downwards, it is increasing to the left of the vertex and decreasing to the right of the vertex.\newlineThe function is increasing on the interval (,2)(-\infty, 2) and decreasing on the interval (2,)(2, \infty).
  7. Name transformation: Name at least one transformation that has been applied to the parent function f(x)=x2f(x) = x^2 to obtain f(x)=(x2)2+5f(x) = -(x - 2)^2 + 5.\newlineThe function has been translated 22 units to the right and 55 units up from the parent function. Additionally, it has been reflected across the xx-axis due to the negative sign in front of the squared term.

More problems from Reflections of functions