Question 199466
<font face="Tahoma" size=1.5>
</pre><font size=4><b>
Given: f (x) = 3x^2 + 6x - 7 , where{{{system(a=3,b=6,c=-7)}}}
For the Vertex:
{{{x=-b/2a=-6/(2*3)=-6/6=red(-1)}}}, X-Intercept (-1,0)


Subst. x=-1 into the eqn for Y-Intercept:
{{{y=3(-1)^2+6(-1)-7}}}
{{{y=3(1)-6-7=3-6-7}}}
{{{y=red(-10)}}}, Y-Intercept (0,-10)


Vertex @ <font color=blue> (-1,-10)</font>



Solving the Quadratic Eqns to find the X-Intercepts of the graph:
{{{3x^2+6x-7=0}}}
Solving for the discriminant: {{{b^2-4ac=6^2-4(3)(-7)=36+84=red(120)}}}


Then,
{{{x=(-6+-sqrt(120))/(2*3)=(-6+-10.95))/6}}}
{{{x=(-6+10.95)/6=4.95/6=red(0.825)}}}
{{{x=(-6-10.95)/6=-16.95/6=red(-2.825)}}}


X-Intercepts: <font color=blue>(0.825,0) & (-2.825,0)</font>



For Y-Intercept, Let Fx=0:
{{{y=3(0)^2+6(0)-7}}}
{{{red(y=-7)}}}, Y-Intercept <font color=blue> (0,-7)</font>

{{{drawing(400,400,-5,5,-15,10,grid(1),graph(400,400,-5,5,-15,10,3x^2+6x-7),green(circle(0.825,0,.12)),green(circle(-2.825,0,.12)),green(circle(0,-7,.12)),blue(circle(-1,-10,.12)))}}}


Thank you,
Jojo</font>