The answer is a = 1, b = 2, and c = -3. How just by look at the points? C is intuitive, but I don't get the other points.
3 Answers
Explanation:
just to explain
if you want to find the
Now, because we are dealing with the form of
the differentiate is always in the form of
now we say (in general):
So as we see, the x_max or x_min is always
Explanation:
#"one possible approach"#
#c=-3larrcolor(red)"y-intercept"#
#• " sum of roots "=-b/a#
#• " product of roots "=ca#
#"here the roots are "x=-3" and "x=1#
#"that is where the graph crosses the x-axis"#
#rArr-3xx1=carArrca=-3rArra=-3/(-3)=1#
#rArr-b/a=-3+1=-2rArrb=2#
#rArry=x^2+2x-3#
graph{x^2+2x-3 [-10, 10, -5, 5]}
Bit wordy but work you way through it. Full explanation given.
Explanation:
Given the standardised form
The curve at the bottom has the special name (what doesn't in maths) of Vertex.
If there are x-intercepts (where the graph crosses the x-axis) then the Vertex value of
Looking at the graph the x-intercepts are at
So the
This is what relates
Write as
Divide both side by
Substitute into
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lets pick a known point.
I choose the left hand x-intercept
Known that
Substitution into
Add 3 to both sides and simplify the brackets
Thus
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that:
is the beginnings of completing the square.