Question

Graphing quadratic equation

Answer 1

Check the attached graph below.

Explanation:

Let us consider the quadratic function

`f\left(x\right)\:=\:2x^2\:-\:12x\:+\:16`

Observe that

`a\:=\:2,\:b\:=\:-12,\:c\:=\:16`

As the value of
`a` is positive.

i.e.
`a=2`

so, it would be an upward (U-shaped) graph.

Now, calculating the value of '
`h`'.

`h=(-b)/(2a)`

`=(-\left(-12\right))/(\left(2\cdot \:\:2\right))`

`= 3`

Then calculating
`k` (using
`h=3`)

`k = f(3)`

`=\:2\left(3\right)^2\:-\:12\cdot 3\:+\:16`

`= 18-36+16`

`= -2`

Now, plotting the graph, and the graph is attached below.

From the graph, it is clear that,

• 
  `\mathrm{X\:Intercepts}:\:\left(4,\:0\right),\:\left(2,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:16\right)`

• The parabola is upward.

• The parabola vertex is
  `\left(3,\:-2\right)`

Please check the attached graph below.