Question

Graph the parabola . y = - 3x ^ 2 - 6x + 4 Plot five points on the parabolathe vertextwo points to the left of the vertex, and two points to the right of the vertexThen click on the graph-a-function button

Answer 1

Answer:

The 5 points: (-1, 7), (0, 4), (-2, 4), (-2.5275, 0), (0.5275, 0)

See the graph below

Step-by-step explanation

Given:

`y\text{ = -3x}^2\text{ - 6x + 4}`

To find:

plot 5 points on the parabola: the vertex, two points before it, and two points after

First, we need to find the vertex point:

`\begin{gathered} vertex\text{ = \lparen h, k\rparen} \\ h\text{ = }(-b)/(2a) \\ k\text{ = f\lparen-b/2a\rparen} \\ \\ a\text{ = -3, b = -6, c = 4} \\ h\text{ = }(-(-6))/(2(-3))=\text{ 6/-6} \\ h\text{ = -1} \\ \\ k\text{ = f\lparen-b/2a\rparen = f\lparen h\rparen} \\ we\text{ will substitute the value of h into the function} \\ k\text{ = -3\lparen-1\rparen}^2\text{ - 6\lparen-1\rparen + 4} \\ k\text{ = -3\lparen1\rparen + 6 + 4} \\ k\text{ = 7} \\ \\ The\text{ vertex \lparen h, k\rparen = \lparen-1, 7\rparen} \end{gathered}`

Next, let's find the y-intercept:

it is the value of y when x = 0

`\begin{gathered} y\text{ = -3\lparen0\rparen}^2\text{ - 6\lparen0\rparen + 4} \\ y\text{ = 4} \\ The\text{ point will be \lparen0, 4\rparen} \\ \\ when\text{ x = -2} \\ y\text{ = -3\lparen-2\rparen}^2\text{ -6\lparen-2\rparen + 4} \\ y\text{ = -12 + 12 +4} \\ y\text{ = 4} \\ The\text{ point will be \lparen-2, 4\rparen} \end{gathered}`

To get the remaining two points, we will use x-intercept

It is the value of x when y = 0

`\begin{gathered} 0\text{ = -3x}^2\text{ - 6x + 4} \\ $$x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$ \\ a\text{ =-3, b = -6, c = 4} \\ \\ x\text{ = }(-(-6)\pm√((-6)^2-4(-3)(4)))/(2(-3)) \\ \\ x\text{ = }(6\pm√(36+48))/(-6)\text{ = }(6\pm√(84))/(-6) \\ \\ x\text{ = }(6\pm9.165)/(-6) \\ \\ x\text{ = }(6+9.165)/(-6)\text{ = }(6-9.165)/(-6) \\ x\text{ = }(15.165)/(-6)\text{ or }(-3.165)/(-6) \\ \\ x\text{ = -2.5275 or 0.5275} \end{gathered}`

The two points: (-2.5275, 0) and (0.5275, 0)

Plotting the points: