Question

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Answer 1

The vertex of the given parabola is (h, k)=(0,0).

(x, y)=(2, -4) is a point on the parabola.

The vertex form of a parbola is,

`y=a(x-h)^2+k\text{ ------(1)}`

Here, (h, k) is the vertex of parabola.

Put h=0, k=0, x=2 and y=-4 in the above equation.

`\begin{gathered} -4=a(2-0)+0 \\ (-4)/(2)=a \\ -2=a \end{gathered}`

Put a=-2, h=0, k=0 in equation (1) to find the function.

`y=-2x^2`

Put y=0 to obtain a quadratic function and solve for x.

`\begin{gathered} 0=-2x^2 \\ x=0 \end{gathered}`

So, there is only one solution to the graph.

Short cut:

Since the parabola touches the x axis when the x intercept is zero, the solution of the quadratic function of the parabola is x=0. So, there is only one solution to the graph.