Question

Plot the given parabola on the axes. Plot the roots, the vertex and two other points.

Answer 1

Step 1:

The first two points are the roots of the parabola.

To get the roots of the parabola, equate y = 0

`\begin{gathered} \text{y = x}^2\text{ + 2x - 35} \\ x^2\text{ + 2x - 35 = 0} \\ x^2\text{ + 7x - 5x - 35 = 0} \\ x(x\text{ + 7)-5(x + 7) = 0} \\ (x\text{ + 7)(x - 5) = 0} \\ x\text{ = -7 , x = 5} \\ \text{The parabola intercept x-axis at (-7, 0) and (5 , 0)} \end{gathered}`

Step 2:

Find the y-intercept.

To find the y-intercept, plug x = 0

`\begin{gathered} \text{y = x}^2\text{ + 2x - 35} \\ y=0^2\text{ + 2}*0\text{ - 35} \\ y\text{ = -35} \\ y-\text{intercept is (0 , -35)} \end{gathered}`

Step 3:

Find the vertex

`\begin{gathered} \text{The vertex is (}(-b)/(2a)\text{ , y)} \\ b\text{ = 2, a = 1} \\ x\text{ = }(-b)/(2a) \\ x\text{ = }(-2)/(2*1) \\ x\text{ = }(-2)/(2) \\ x\text{ = -1} \\ y=(-1)^2\text{ + 2(-1) - 35} \\ y\text{ = 1 - 2 - 35} \\ y\text{ = -36} \\ \text{Vertex = (-1, -36)} \end{gathered}`

Final answer

All the five points are:

Roots (x-intercept) = (-7, 0) , (5 , 0)

y-intercept = (0, -35)

vertex = (-1, -36)

Other point = (-5, -20)