So can you use the discriminant ?
And it factorises to
So you have the two x-intercepts.
Now you need the vertex (where the derivative is 0) to draw the graph !
sketch the graph of the following equation
I rearranged the equation to
but i am stuck here cause can't seem to factor the equation, and i am not meant to use the quadratic equation or completing the square.
how do i facto this?
i tried but that does not work
You should find the maxima/minima and intersections with x-axis. You can rewrite the function:
And the final :-)
So there is minus on the right side of the equation so it is parabola inverted by x-axis. Its maximum is in point
Intersection points you'll find by discriminant.
for a quadratic of the form the vertex occurs where . of course you can find the corresponding y-value by plugging in the x-value for the vertex
basically I am meant to sketch the graph by firstly putting y=0 to find the x-axis crossing points coordinates and than put x=0 to find the y crossing points coordinates.
and cause and there are two different roots.
but i can't daw the graph as i am not able to factorise the eqution to solve for x ?
does anybody understand what i am meant to do now?
(I'm sure you know how to do that)
Next I would make a table of values
Ex take the x values -4,-3,-2,-1,0,1,2 and plug it into the equation to solve for the different y values. (there will not be the exact vertex co-ordinates, although it will be very close.) Then simply plot the points and you're done!