Question 107371
<pre>
I need help with this kind of problem:
Find the vertex, the y-intercept, and symmetric point, and use these to sketch a graph.
y=2x^2 -11x -12
I am having problems solving for the vertex.
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Formula for the x-coordinate of the vertex of a parabola: {{{x = - b/(2a)}}} 
{{{y = highlight(2)x^2 * highlight_green(- 11)x - 12}}}. Compare to:
{{{y = highlight(a)x^2 * highlight_green(b)x + c}}}
In this case, b = - 11, and a = 2.
So, the x-coordinate of the vertex of THIS parabola is:{{{- (- 11)/(2*2) = 11/4}}}

Now, substitute the x-value into the ORIGINAL equation to get the y-coordinate of the vertex, as follows: 
{{{y = 2x^2 - 11x - 12}}}
{{{y = 2(11/4)^2 - 11(11/4) - 12}}}
{{{y = 2(121/16) - 121/4 - 12}}}
{{{y = 121/8 - 121/4 - 12}}}
{{{y = (121 - 242 - 96)/8}}}
{{{y = (- 217)/8}}} <==== y-coordinate of the vertex of THIS parabola
<font color = red><font size = 4><b>Vertex</font></font></b> of parabolic equation, {{{matrix(1,3, y, "=", 2x^2 - 11x - 12)}}}: {{{matrix(1,3, highlight("(x, y)"), "=", highlight(matrix(1,5, "(", 11/4, ",", (- 217)/8, ")")))}}}</pre>