Question

In the xy-plane, the graph of y = 3x^2 -14x intersects the graph of y = 2 at the points (0,0) and (a, a). What is the value of a?

Answer 1

We have a parabola

`y=3x^2-14x`

and a line y=2

If we graph the two functions we obtain

we can obtain the ordered pairs where the equations intercept each other when y=2 in the parabola equation and finding the values of x

`2=3x^2-14x`

Solving the equation we find two values for x so we have

`\begin{gathered} x_1=-0.14 \\ x_2=4.8 \end{gathered}`

the ordered pairs are

(-0.14,2) and (4.8,2)

as we can see the points given in the question are wrong because at the points given the value of y will be different to 2, for example in (0,0 ) the line and the parabola do not intersect each other.