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Activity 12 Notes Name Graphing Quadratic Functions in Standard Form (Activity 12) Standard Form of a Quadratic Function f × x) ax 2 + bx + c Axis of Symmetry: x b 2a b Vertex:, 2a b f 2a Graphing
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How to fill out graphing quadratic functions in
How to fill out graphing quadratic functions in:
01
Start by identifying the quadratic function equation. This equation will be in the form of y = ax^2 + bx + c, where a, b, and c are constants.
02
Determine the vertex of the quadratic function. The vertex is given by the formula x = -b/2a. Substitute the values of a and b from the equation into the formula to find the x-coordinate of the vertex.
03
Once you have the x-coordinate of the vertex, substitute it back into the equation to find the y-coordinate. This will give you the coordinates of the vertex.
04
Plot the vertex on the coordinate plane.
05
Determine the x-intercepts or roots of the quadratic function. These are the values of x for which the function is equal to zero. Use the quadratic formula or factor the equation to find the roots.
06
Plot the x-intercepts on the coordinate plane.
07
Determine the y-intercept of the quadratic function. This is the value of y when x = 0. Substitute 0 for x in the equation and solve for y.
08
Plot the y-intercept on the coordinate plane.
09
To further sketch the graph, either use symmetry or calculate additional points on either side of the vertex. Substitute different values of x into the equation and solve for y.
10
Connect the plotted points to obtain the graph of the quadratic function.
Who needs graphing quadratic functions in:
01
Mathematics students studying algebra or pre-calculus courses need to understand and graph quadratic functions as they are fundamental in these subjects.
02
Scientists and engineers often encounter quadratic functions when modeling physical phenomena. Graphing these functions helps them visualize and analyze the data.
03
Individuals involved in finance, economics, and data analysis can benefit from graphing quadratic functions as they often deal with parabolic curves that represent various trends and relationships.
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