Question

Use the Parabola tool to graph the quadratic function.

f(x)=3x^2−6x+5

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answer 1

graphed below:

$\sf f(x)=3x^2-6x+5$

• vertex: (1, 2)

• cuts y-axis: (0, 5)

Answer 2

Answer:

Given function:    $f(x)=3x^2-6x+5$

Vertex form:  $y=a(x-h)^2+k$  

(where $(h, k)$ is the vertex)

Expand vertex form:

$y=ax^2-2ahx+ah^2+k$

Compare coefficients of given function with expanded vertex form

Comparing coefficient of $x^2$:

$3=a$

Comparing coefficient of $x$:

$\ \ \ \ \ -6=-2ah\\\implies-6=-2 \cdot 3h\\\implies -6=-6h\\\implies h=1$

Comparing  constant:

$\ \ \ \ \ \ 5=ah^2+k\\\implies5=3(1)^2+k \\\implies 5=3+k\\\implies k=2$

Therefore, the vertex is (1, 2)

As the leading coefficient is positive, the parabola will open upwards.

Additional plot points:

$f(0)=3(0)^2-6(0)+5=5$

$f(2)=3(2)^2-6(2)+5=5$

(0, 5) and (2, 5)