Name: Chapter Review: Graphing Quadratic Functions A. Intro to Graphs of Quadratic Equations: = ax + bx+ c A is a function that can be written in the form = ax + bx+ c where a, b, and c are real numbers and a 0. Ex: = x = x + = x x The graph of a quadratic function is a U-shaped curve called a. The maximum or minimum point is called the Identif the vertex of each graph; identif whether it is a minimum or a maximum..).) Vertex: (, ) Vertex: (, ).).) Vertex: (, ) Vertex: (, ) B. Ke Features of a Parabola: = ax + bx+ c Direction of Opening: When a > 0, the parabola opens : When a < 0, the parabola opens : Width: When a <, the parabola is than When a =, the parabola is the width as When a >, the parabola is than = x = x = x Vertex: The highest or lowest point of the parabola is called the vertex, which is on the axis of b smmetr. To find the vertex, plug in x = and solve for. This ields a point (, ) a b Axis of smmetr: This is a vertical line passing through the vertex. Its equation is: x = a x-intercepts: are the 0,, or points where the parabola crosses the x-axis. Plug in = 0 and solve for x. -intercept: is the point where the parabola crosses the -axis. Plug in x = 0 and solve for.
Without graphing the quadratic functions, complete the requested information:.) f( x) = x x+.) gx ( ) = x+ x What is the direction of opening? What is the direction of opening? Is the vertex a max or min? Is the vertex a max or min? Wider or narrower than = x? Wider or narrower than = x?.) = x.) = x + x 0... What is the direction of opening? Is the vertex a max or min? Wider or narrower than = x? What is the direction of opening? Is the vertex a max or min? Wider or narrower than = x? The parabola = x is graphed to the right. Note its vertex (, ) and its width. You will be asked to compare other parabolas to this graph. C. Graphing in STANDARD FORM ( = ax + bx+ c): we need to find the vertex first. Vertex Graphing - list a =, b =, c = - put the vertex ou found in the center of b our x- chart. - find x = - choose x-values less than and x-values more a - plug this x-value into the function (table) than our vertex. - this point (, ) is the vertex of the parabola - plug in these x values to get more points. - graph all points Find the vertex of each parabola. Graph the function and find the requested information.) f(x)= -x + x + a =, b =, c = 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Max or min? Axis of smmetr: Compare to the graph of = x
0.) h(x) = x + x + 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Max or min? Axis of smmetr: Compare to the graph of = x.) k(x) = x x 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Max or min? Axis of smmetr: Compare to the graph of = x.) State whether the function = x + x has a minimum value or a maximum value. Then find the minimum or maximum value..) Find the vertex of = x + x. State whether it is a minimum or maximum. Find that minimum or maximum value.
Another useful form of the quadratic function is the vertex form:. GRAPH OF VERTEX FORM = a(x h) + k The graph of = a(x h) + k is the parabola = ax translated h units and k units. The vertex is (, ). The axis of smmetr is x =. The graph opens up if a 0 and down if a 0. Find the vertex of each parabola and graph. = x+.) ( ) 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Max or min value: Compare width to = x : Axis of smmetr: = x +.) ( ) 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Max or min value: Compare width to = x : Axis of smmetr:
.) g(x) = -x + x 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Max or min value: Compare width to = x : Axis of smmetr:.) = x + x + 0-0 - - - - - - - - - - 0 x - - - - - - - - -0.) = x + x 0-0 - - - - - - - - - - 0 x - - - - - - - - -0
.) = x +x = x +x + 0 0.) = -x + = x x 0-0 - - - - - - - - - - 0 x - - - - - - - - -0.) Find the zeros of the quadratic function shown.
REVIEW!! To graph a quadratic function, ou must FIRST find the vertex (h, k)!! If the function starts in standard form = ax + bx+ c: st b : The x-coordinate of the vertex, h, = a nd : Find the -coordinate of the vertex, k, b plugging the x-coordinate into the function & solving for. AFTER finding the vertex: Use the a value to plot more points using the pattern up,,, - OR - Make a table of values with points: The vertex, plug in x-coordinates SMALLER than the x-coordinate of the vertex & x-coordinates LARGER than the x-coordinate of the vertex. Direction of Opening: If a is positive, the graph opens up If a is negative, the graph opens down. Width of the function: If a >, the graph is narrower than If a <, the graph is wider than = x = x Graph each function. (A) State the vertex. (B) State the direction of opening (up/down). (C) State whether the graph is wider, narrower, or the same width as = x..) f( x) = ( x+ ) 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Compare width to the graph of = x
.) k(x) = x + x + 0-0 - - - - - - - - - - 0 x - - - - - - - - -0.) f(x) = x x Compare width to the graph of = x 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Compare width to the graph of = x.) f( x) = x + x+ 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Compare width to the graph of = x
.) hx ( ) = x + x+ 0-0 - - - - - - - - - - 0 x - - - - - - - - -0.) g(x) = (x ) + Compare width to the graph of = x 0-0 - - - - - - - - - - 0 x - - - - - - - - -0 Compare width to the graph of = x For questions -0, label the vertex and axis of smmetr.. = x x+. = x x+ 0. ( ) x =