Determine Maximum and Minimums of Functions

Does this graph have a maximum or minimum?

• Minimum

• Maximum

What is the arrow pointing at? How can you use this value?

• The arrow is pointing at the y-intercept. The x-value is the axis of symmetry and the y-value of this point is equivalent to the maximum/minimum 

• The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum and the y-value is the axis of symmetry

• The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum

• The arrow is pointing at the vertex. The x-value is the axis of symmetry and the y-value is equivalent to the minimum/maximum

Does this parabola have a maximum or minimum?

• Maximum

• Minimum

Which answer choice describes  y = -3x² +7x - 2 accurately?

• opens up with a maximum

• opens up with a minimum

• opens down with a maximum

• opens down with a minimum 

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

• Minimum value, because the a value is positive

• Maximum value, because the b value is positive

• Maximum value, because the a value is positive

• Minimum value, because the c value is negative

What is the green dot on the parabola called?

• maximum

• minumum

• roots

• zeros

Does y = -4x² have a maximum or minimum value?

• maximum

• minimum

Identify the vertex and whether the graph opens up or down.

• (-1, 4); opens up

• (-1, 4); opens down

• (1, 4); opens up

• (1, 4); opens down

How many extrema are there in this graph?

• 2 max, 2 min

• 3 max, 2 min

• 2 man, 3 min

• 3 increasing intervals, 2 decreasing intervals

• 2 increasing intervals, 3 decreasing intervals

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

CCSS.MATH.CONTENT.HSF.IF.C.7.c

• 0

• 1

• 4

• -1

• 2

• 5

Answer explanation

To find extrema, we calculate the derivative f'(x) = -6x^2 + 24x - 8 and set it to zero. Solving gives x = 0, 1, and 4. The relative minimum occurs between x = 0 and x = 1, and the relative maximum is at x = 4.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

CCSS.MATH.CONTENT.HSF.IF.C.7.c