Use the Parabola tool to graph the quadratic function. f(x)=2x^2−12x+19 Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

To find the vertex of our parabola, we are going to use the vertex formula: For a quadratic of the form [tex]f(x)=x^2+bx+c[/tex] it vertex [tex](h,k)[/tex] is given by [tex]h= \frac{-b}{2a} [/tex], [tex]k=f(h)[/tex].
We can infet from our parabola that [tex]a=2[/tex] and [tex]b=-12[/tex]. So lets replace those values in our formula:
[tex]h= \frac{-b}{2a} [/tex]
[tex]h= \frac{-(-12)}{2(2)} [/tex]
[tex]h= \frac{12}{4} [/tex]
[tex]h=3[/tex]
[tex]k=f(h)=2(3)^2-12(3)+19[/tex]
[tex]k=2(9)-36+19[/tex]
[tex]k=18-17[/tex]
[tex]k=1[/tex]
The vertex [tex](h,k)[/tex] of our parabola is [tex](3,1)[/tex]

Now to find our second point, we are going to evaluate our parabola at [tex]x=0[/tex]
[tex]f(0)=2(0)^2-12(0)+19[/tex]
[tex]f(0)=0+0+19[/tex]
[tex]f(0)=19[/tex]
Our second point is [tex](0,19)[/tex]

We can conclude that we can graph the parabola [tex]f(x)=2x^2-12x+19[/tex] using its vertex [tex](3,1)[/tex] and the point [tex](0,19)[/tex] as follows:

jainveenamrata jainveenamrata · Answer 2 · 2022-06-20T09:26:35+02:00

The vertex of the parabola f(x) = 2(x − 3)² + 1 is at (3, 1). The graph is given below.

What is the parabola?

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Use the Parabola tool to graph the quadratic function.

f(x) = 2x² − 12x + 19

Then take common, we have

f(x) = 2(x² − 6x) + 19

Add and subtract 3², then we have

f(x) = 2(x² − 6x + 3²) - 18 + 19

f(x) = 2(x − 3)² + 1

The graph is given below.

More about the parabola link is given below.

https://brainly.com/question/8495504

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