Question

How do you use the important points to sketch the graph of `y = x^2 + 4x − 21`?

Answer 1

`x`-intercepts: `(-7, 0), (3, 0)`
`y`-intercept: `(0, -21)`
vertex: `(-2, 25)`

Explanation:

Given: `y = x^2 + 4x - 21`

To find `y`-intercept: set `x = 0: " "y = -21`

To find `x`-intercepts: set `y = 0` and factor:

`x^2 + 4x - 21 = 0`

`(x +7)(x - 3) = 0`

`x + 7 = 0; x = -7 " and " x - 3 = 0; x = 3`

To find the vertex and axis of symmetry , put the equation in `Ax^2 + Bx + C = 0` form, let `x = (-B)/(2A)` and solve for `y`:

`x = -4/2 = -2 " "` This is the axis of symmetry

`y = (-2)^2 + 4(-2) -21 = 4 - 8 - 21 = -25`

vertex: `(-2, 25)`

graph{x^2+4x-21 [-64.4, 52.63, -28.33, 30.17]}