ratic Functions- No Graphing CalculatorName:when necessary. You must use correct notation for full credit.Date:Pavlinaey Featuresthe key features of the following graph.2) y-intercep3) Axis of Symmetry:5) Domain::R7) Increasing:4) Vertex:6) Range::R8) DecreForm:asked to graph f(x)=−(x−2)2+5 and produced the following gya) Name at least one transformatic
Q. ratic Functions- No Graphing CalculatorName:when necessary. You must use correct notation for full credit.Date:Pavlinaey Featuresthe key features of the following graph.2) y-intercep3) Axis of Symmetry:5) Domain::R7) Increasing:4) Vertex:6) Range::R8) DecreForm:asked to graph f(x)=−(x−2)2+5 and produced the following gya) Name at least one transformatic
Identify y-intercept: Identify the y-intercept of the function f(x)=−(x−2)2+5.The y-intercept occurs where x=0. Substitute x=0 into the function to find the y-intercept.f(0)=−(0−2)2+5f(0)=−(−2)2+5f(0)=−4+5f(0)=1The y-intercept is the point (0,1).
Determine axis of symmetry: Determine the axis of symmetry for the function f(x)=−(x−2)2+5.The axis of symmetry for a parabola in the form f(x)=a(x−h)2+k is the vertical line x=h. Here, h=2.The axis of symmetry is the line x=2.
Find vertex: Find the vertex of the function f(x)=−(x−2)2+5.The vertex of a parabola in the form f(x)=a(x−h)2+k is the point (h,k). Here, h=2 and k=5.The vertex is the point (2,5).
Determine domain: Determine the domain of the function f(x)=−(x−2)2+5. The domain of any quadratic function is all real numbers, denoted as (−∞,∞) or R.
Determine range: Determine the range of the function f(x)=−(x−2)2+5.Since 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.The range is (−∞,5].
Identify intervals: Identify the intervals where the function f(x)=−(x−2)2+5 is increasing and decreasing.Since the parabola opens downwards, it is increasing to the left of the vertex and decreasing to the right of the vertex.The function is increasing on the interval (−∞,2) and decreasing on the interval (2,∞).
Name transformation: Name at least one transformation that has been applied to the parent function f(x)=x2 to obtain f(x)=−(x−2)2+5.The function has been translated 2 units to the right and 5 units up from the parent function. Additionally, it has been reflected across the x-axis due to the negative sign in front of the squared term.