Question

In the x-y plane, the point (3,1) lies on the graph of the function g. If g(x) = a - 2 x^2, where a is a constant, what is the value of a ?

Answer 1

The points on the graph of a function are all of the form

$(x,g(x))$

In fact, the graph is composed by all points $(x,y)$ such that y is the image of x, as written above.

So, if $(3,1)$ lies on graph, it means that $g(3)=1$.

Since we know the expression for $g(x)$, we can plug the values:

$g(3) = a-2(3)^2 = a-18 = 1$

We can solve for $a$ by adding 18 to both sides to get $a=19$.

So, the expression for the function is $g(x) = 19-2x^2$