Question

Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept: (0,-1) I -1 4 Z Q Ó y =

Answer 1

The equation of a parabola in factored form is:

`y=a(x-x_1)(x-x_2)`

where a is the leading coefficient, and x1 and x2 are the zeros of the parabola.

From the graph, we can see that the zeros (the x-intercepts) are x1 = -1 and x2 = 4. We also know that when x = 0, y = -1 (from the y-intercept), replacing this information into the above equation, we get:

`\begin{gathered} -1=a\cdot(0-(-1))\cdot(0-4) \\ -1=a\cdot1\cdot(-4) \\ -1=a\cdot(-4) \\ (-1)/(-4)=a \\ (1)/(4)=a \end{gathered}`

Finally, the equation of the parabola is:

`\begin{gathered} y=(1)/(4)(x-(-1))(x-4) \\ y=(1)/(4)(x+1)(x-4) \end{gathered}`