Question

Use the parabola tool to graph the quadratic function. f(x)=2x2+12x+16

Answer 1

Answer:

Step-by-step explanation:

To obtain the graph of a parabola, three data are necessary: ​​the vertex (the vertex is the highest or lowest point of the graph corresponding to the parabola and there it is on the plane of symmetry of the parabola), the roots ( those values ​​of x for which the expression is 0. Graphically,  the roots correspond to the abscissa of the points where the parabola  cuts the x-axis.) and the concavity.

Being f(x)=ax²+bx+c, you can see that, in this case, a=2, b=12 and c=16. So:

• Vertex= for your calculation, $xv=\frac{-b}{2*a}=\frac{-12}{2*2}$, so xv=-3. Now that you know x, all you have to do is enter its numerical value into the original formula to find yv. yv=2*(-3)²+12*(-3)+16. Then yv=-2

• Roots:  The roots are calculated using the expression: $x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}$. Replacing the values that you have:$x1,x2=\frac{-12+-\sqrt{12^{2}-4*2*16 } }{2*2}$ Solving, you obtain x1=-2 and x2=-4
• Concavity: If a> 0 (positive) the parabola is concave or pointed upwards, while if a <0 (negative) the parabola is convex or pointed downwards. In this case a = 2, so the parabola opens upward, being concave.

In this way, the graph shown in the attached image is obtained.

Answer 2

We have that
f(x)=2x²+12x+16

using a graph tool
see the attached figure