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Name

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Date

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Algebra
8.1-8.4 test review
In Exercises 1 and 2, identify characteristics of the quadratic function and its graph.
1.
2.
In Exercises 3-8, graph the function. Compare the graph to the graph of 
f(x)=x^(2).
3. 
g(x)=5x^(2)
4. 
quad k(x)=(2)/(3)x^(2)
Up/down
up/down
AoS 
qquad
Vertex 
qquad
Max/Min
D: 
qquad
R: 
qquad

Name\newline \qquad \newlineDate\newline \qquad \newlineAlgebra\newline88.118-8.44 test review\newlineIn Exercises 11 and 22, identify characteristics of the quadratic function and its graph.\newline11.\newline22.\newlineIn Exercises 338-8, graph the function. Compare the graph to the graph of f(x)=x2 f(x)=x^{2} .\newline33. g(x)=5x2 g(x)=5 x^{2} \newline44. k(x)=23x2 \quad k(x)=\frac{2}{3} x^{2} \newlineUp/down\newlineup/down\newlineAoS \qquad \newlineVertex \qquad \newlineMax/Min\newlineD: \qquad \newlineR: \qquad

Full solution

Q. Name\newline \qquad \newlineDate\newline \qquad \newlineAlgebra\newline88.118-8.44 test review\newlineIn Exercises 11 and 22, identify characteristics of the quadratic function and its graph.\newline11.\newline22.\newlineIn Exercises 338-8, graph the function. Compare the graph to the graph of f(x)=x2 f(x)=x^{2} .\newline33. g(x)=5x2 g(x)=5 x^{2} \newline44. k(x)=23x2 \quad k(x)=\frac{2}{3} x^{2} \newlineUp/down\newlineup/down\newlineAoS \qquad \newlineVertex \qquad \newlineMax/Min\newlineD: \qquad \newlineR: \qquad
  1. Identify Parabola Direction: Identify the direction of the parabola for g(x)=5x2g(x)=5x^{2}. Since the coefficient of x2x^2 is positive, the parabola opens upwards.
  2. Determine Stretch Factor: Determine the stretch factor for g(x)=5x2g(x)=5x^{2}.\newlineThe coefficient 55 indicates that the parabola is stretched vertically by a factor of 55 compared to f(x)=x2f(x)=x^{2}.
  3. Find Axis of Symmetry: Find the axis of symmetry (AoS) for g(x)=5x2g(x)=5x^{2}.\newlineThe AoS is x=0x=0 because the equation is in standard form and symmetric about the y-axis.
  4. Identify Vertex: Identify the vertex for g(x)=5x2g(x)=5x^{2}.\newlineThe vertex is at the origin (0,0)(0,0) since there are no horizontal or vertical shifts.
  5. Determine Vertex Type: Determine if the vertex is a maximum or minimum for g(x)=5x2g(x)=5x^{2}.\newlineSince the parabola opens upwards, the vertex is a minimum.
  6. State Domain: State the domain DD for g(x)=5x2g(x)=5x^{2}.\newlineThe domain of any quadratic function is all real numbers, so D:(,)D: (-\infty, \infty).
  7. State Range: State the range (R)(R) for g(x)=5x2g(x)=5x^{2}. Since the parabola opens upwards and the vertex is at (0,0)(0,0), the range is [0,)[0, \infty).

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