Question

Sketch and graph the function pls I need help sorry it’s a terrible graph but y’all got computer graphs

Answer 1

Given the function:

`-3x^2-12x-10`

In order to graph the quadratic function, we find some points on the parabola.

Vertex

Using the vertex formula:

`\begin{gathered} \text{Vertex}=(-(b)/(2a),(4ac-b^2)/(4a)) \\ =(-(-12)/(2*-3),(4(-3)(-10)-(-12)^2)/(4*-3)) \\ =(-2,2) \end{gathered}`

y-intercept

When x=0

`\begin{gathered} y=-3(0)^2-12(0)-10=-10 \\ \implies(0,-10) \end{gathered}`

Next, look for one point to the right of the vertex and one to the left.

When x=-1

`\begin{gathered} y=-3(-1)^2-12(-1)-10=-3+12-10=-1 \\ \implies(-1,-1) \end{gathered}`

Similarly, when x=-3

`\begin{gathered} y=-3(-3)^2-12(-3)-10=-27+36-10=-1 \\ \implies(-3,-1) \end{gathered}`

Similarly, when x=-4

`\begin{gathered} y=-3(-4)^2-12(-4)-10=-48+48-10=-10 \\ \implies(-4,-10) \end{gathered}`

The graph showing the points (-2,2), (0,-10), (-1,-1), (-3,-1) and (-4,-10) is attached below: