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?
enter your response here
(Type an ordered pair. Use integers or fractions for any numbers in the expression.)
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).
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.)
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).
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.)
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).