Show that a = 2 in quadratic function

Feb 2019
4
1
South Africa
I'm studying for a test and doing old exam papers to which I do not have answer sheets for and my textbook doesn't have an example of this sort of question, a is always given in my books. I'm not sure how to approach this question that asks me to show that a = 2 in the quadratic function for the parabola y = ax^2-x-6, any help on how I should start, please?

It's a sketch of an upwards curving parabola (f) and a straight line (g). The parabola has a vertex B, it cuts the x-axis at (0,2) and the other x-intercept is only given as D. The y-intercept therefore is (0,-6), right?

g cuts the parabola at point E on the y-axis and at A. the equation for g is given as g(x) = y=x+c

Any tips on how to find a in y=ax^2-x-6?

Thanks in advance :)
 
Apr 2018
163
38
Sukoharjo
Try substituting the known coordinates to the quadratic function.
 
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Jun 2013
1,112
590
Lebanon
cuts the x-axis at $(2,0)$ not $(0,2)$

replace \(\displaystyle x=2\) and \(\displaystyle y=0\) in the equation of the parabola

$$y=a x^2-x-6$$
 
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