Week 8 Mat117 concept check
Explain a process you would use to graph a quadratic equation. Include how to find the x-intercepts, the vertex, and the axis of symmetry.
EXAMPLE:
For the function, f(x) = (x+5)2 - 3 = (x+5)(x+5) - 3 = x2 + 10x + 25
This function follows the form: f(x) = ax2 + bx + c , where "a" cannot equal zero.
The questions that you need to answer when graphing any quadratic equation:
a)The value of a
b)Does the parabola open up or down? If ax2 opens up it means it is positive, and if ax2 opens down it is negative.
c)Does the parabola have a minimum or maximum value? If it opens up it has a minimum value, however, if it opens down it has a maximum value.
d)Vertex (vertex is where the tip of the curve is, you will always have a (x,y) for vertex.)
e)The minimum or maximum value (this is always y value at vertex)
f)The Axis of Symmetry ( the line that you can draw down the center of the parabola and cut it in half to make two mirror images)
g)The x-intercept(s) (what x is when y equals zero) (x,0)
h)The y-intercept(s) ( what y is when x equals zero) (0,y)
i)Two additional points that lie on the graph
j)Graph
k)Domain and Range