The function g(x) is defined by the equation g(x) = -3x² + x - 1. Which is the value of g(1)?
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Answer:
Step-by-step explanation:
A parabola is written in the form
(1)
where:
is the x-coordinate of the vertex of the parabola
is the y-coordinate of the vertex of the parabola
is a scale factor
For the parabola in the problem, we know that the vertex has coordinates (4,-3), so we have:
(2)
From this last equation, we get that (3)
Substituting (2) and (3) into (1) we get the new expression:
(4)
We also know that the parabola contains the point (2,-1), so we can substitute
x = 2
f(x) = -1
Into eq.(4) and find the value of k:
So we also get:
So the equation of the parabola is:
(5)
Now we want to rewrite it in the standard form, i.e. in the form
To do that, we simply rewrite (5) expliciting the various terms, we find: