Question

SHOW YOUR WORK
A quadratic equation is shown below:

3x2 − 11x + 10= 0

Part A: Find the vertex. Show your work.

Part B: Solve for x using an appropriate method. SHOW THE STEPS OF YOUR WORK.

Answer 1

Answer: x=-16/11

6+11x+10=0

We add all the numbers together, and all the variables

11x+16=0

We move all terms containing x to the left, all other terms to the right

11x=-16

x=-16/11

Answer 2

Answer:

Vertex:

Roots: $x=\frac{5}{3}$ or $x=2$

Step-by-step explanation:

The given quadratic equation is:

Let $f(x)=3x^2-11x+10$

We obtain the vertex form by completing the square;

$f(x)=3(x^2-\frac{11}{3}x)+10$

Add and subtract the square of half the coefficient of x.

$f(x)=3(x^2-\frac{11}{3}x+(-\frac{11}{6})^2+10-3(-\frac{11}{6})^2)$

This simplifies to

$f(x)=3(x-\frac{11}{6})^2-\frac{1}{12}$

Hence the vertex is $(\frac{11}{6},-\frac{1}{12})$

We now solve to obtain:

$3(x-\frac{11}{6})^2-\frac{1}{12}=0$

$3(x-\frac{11}{6})^2=\frac{1}{12})$

$(x-\frac{11}{6})^2=\frac{1}{36})$

$(x-\frac{11}{6})=\pm \sqrt{\frac{1}{36}}$

$x=\frac{11}{6}\pm \frac{1}{6}$

$x=\frac{5}{3}$ or $x=2$