Answer:
Check the attached graph below.
Step-by-step explanation:
Let us consider the quadratic function
[tex]f\left(x\right)\:=\:2x^2\:-\:12x\:+\:16[/tex]
Observe that
[tex]a\:=\:2,\:b\:=\:-12,\:c\:=\:16[/tex]
As the value of [tex]a[/tex] is positive.
i.e. [tex]a=2[/tex]
so, it would be an upward (U-shaped) graph.
Now, calculating the value of '[tex]h[/tex]'.
[tex]h=\frac{-b}{2a}[/tex]
[tex]=\frac{-\left(-12\right)}{\left(2\cdot \:\:2\right)}[/tex]
[tex]= 3[/tex]
Then calculating [tex]k[/tex] (using [tex]h=3[/tex])
[tex]k = f(3)[/tex]
[tex]=\:2\left(3\right)^2\:-\:12\cdot 3\:+\:16[/tex]
[tex]= 18-36+16[/tex]
[tex]= -2[/tex]
Now, plotting the graph, and the graph is attached below.
From the graph, it is clear that,
- [tex]\mathrm{X\:Intercepts}:\:\left(4,\:0\right),\:\left(2,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:16\right)[/tex]
- The parabola vertex is [tex]\left(3,\:-2\right)[/tex]
Please check the attached graph below.
