Sketch the graph of the equation. Label the vertex and the intercepts.

Question

yequals3 x squared minus 11 x plus 6
Question content area bottom
Part 1
What is the​ vertex?
  
enter your response here
​(Type an ordered pair. Use integers or fractions for any numbers in the​ expression.)

Answer 1

To find the vertex, we can use the formula for the x-coordinate of the vertex of a quadratic function:

x = -b/(2a), where a = 3 and b = -11 in this case.

So, x = -(-11)/(2 * 3) = 11/6.

Now, we can substitute x = 11/6 into the equation to find the y-coordinate:

y = 3(11/6)^2 - 11(11/6) + 6
y = 3(121/36) - 121/6 + 6
y = 363/36 - 121/6 + 6
y = 11 - 121/6 + 6
y = 11 - 20 + 6
y = -3

Therefore, the vertex is (11/6, -3).

The x-intercepts can be found by setting y = 0:

0 = 3x^2 - 11x + 6

This equation can be factored as (3x - 2)(x - 3) = 0, so the x-intercepts are x = 2/3 and x = 3.

The y-intercept can be found by setting x = 0:

y = 3(0)^2 - 11(0) + 6
y = 6

Therefore, the x-intercepts are (2/3, 0) and (3, 0), and the y-intercept is (0, 6).

Answer 2

That's incorrect.
Correct​ answer:
left parenthesis StartFraction 11 Over 6 EndFraction comma negative StartFraction 49 Over 12 EndFraction right parenthesis
Your​ answer:
left parenthesis StartFraction 11 Over 6 EndFraction comma negative 3 right parenthesis

Sketch the graph of the equation. Label the vertex and the intercepts.
yequals3 x squared minus 11 x plus 6
Question content area bottom
Part 1
What is the​ vertex?
  
left parenthesis StartFraction 11 Over 6 EndFraction comma negative StartFraction 49 Over 12 EndFraction right parenthesis
​(Type an ordered pair. Use integers or fractions for any numbers in the​ expression.)
Part 2
What are the​ x-intercept(s)?
  
enter your response here
​(Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as​ needed.)

Answer 3

To find the x-intercepts, we need to set y = 0 and solve for x:

0 = 3x^2 - 11x + 6

This equation can be factored as (3x - 2)(x - 3) = 0. Setting each factor to zero gives us x = 2/3 and x = 3.

Therefore, the x-intercepts are (2/3, 0) and (3, 0).

Answer 4

Sketch the graph of the equation. Label the vertex and the intercepts.
yequals3 x squared minus 11 x plus 6
Question content area bottom
Part 1
What is the​ vertex?
  
left parenthesis StartFraction 11 Over 6 EndFraction comma negative StartFraction 49 Over 12 EndFraction right parenthesis
​(Type an ordered pair. Use integers or fractions for any numbers in the​ expression.)
Part 2
What are the​ x-intercept(s)?
  
left parenthesis two thirds comma 0 right parenthesis comma left parenthesis 3 comma 0 right parenthesis
​(Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as​ needed.)
Part 3
What is the​ y-intercept?
  
enter your response here
​(Type an ordered pair. Use integers or fractions for any numbers in the​ expression.)

Answer 5

To find the y-intercept, we set x = 0 in the equation:

y = 3(0)^2 - 11(0) + 6
y = 6

Therefore, the y-intercept is (0, 6).