use the vertex and intercepts to sketch the graph of the quadratic function. give the equation for the…

use the vertex and intercepts to sketch the graph of the quadratic function. give the equation for the parabolas axis of symmetry. use the graph to determine the functions domain and range.\nf(x)=6x² + 12x - 1\nwhat is the vertex?\n(-1, -7) (type an ordered pair.)\nwhat are the x - intercepts?\n(type an ordered pair. use a comma to separate answers as needed. round to the nearest hundredth as needed.)

use the vertex and intercepts to sketch the graph of the quadratic function. give the equation for the parabolas axis of symmetry. use the graph to determine the functions domain and range.\nf(x)=6x² + 12x - 1\nwhat is the vertex?\n(-1, -7) (type an ordered pair.)\nwhat are the x - intercepts?\n(type an ordered pair. use a comma to separate answers as needed. round to the nearest hundredth as needed.)

Answer

Explanation:

Step1: Recall the quadratic formula

For a quadratic function (y = ax^{2}+bx + c), the (x) - intercepts are found by solving (ax^{2}+bx + c=0). Here (a = 6), (b = 12), (c=-1). The quadratic formula is (x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}).

Step2: Substitute values into the quadratic formula

First, calculate the discriminant (\Delta=b^{2}-4ac=(12)^{2}-4\times6\times(-1)=144 + 24=168). Then (x=\frac{-12\pm\sqrt{168}}{12}=\frac{-12\pm2\sqrt{42}}{12}=\frac{-6\pm\sqrt{42}}{6}). (\sqrt{42}\approx6.48), so (x_1=\frac{-6 + 6.48}{6}\approx0.08) and (x_2=\frac{-6-6.48}{6}\approx-2.08)

Answer:

((0.08,0),(-2.08,0))