Math Problem Statement
Question content area top
Part 1
How can you find the maximum or minimum value of a quadratic function?
Question content area bottom
Part 1
Choose the correct answer below.
A.
Evaluate the function with
xequals=0.
The resulting y-value is the minimum or maximum value depending on whether the graph opens upward or downward.
B.
Find the vertex. The y-coordinate of the vertex is the minimum or maximum value depending on whether the graph opens upward or downward.
C.
Find the y-intercept. The y-intercept is the minimum or maximum value depending on whether the graph opens upward or downward.
D.
Find the vertex. The x-coordinate of the vertex is the minimum or maximum value depending on whether the graph opens upward or downward.
Solution
The correct answer is:
B. Find the vertex. The y-coordinate of the vertex is the minimum or maximum value depending on whether the graph opens upward or downward.
Explanation:
In the case of a quadratic function , the maximum or minimum value occurs at the vertex of the parabola. The y-coordinate of the vertex represents this value:
- If (the parabola opens upwards), the vertex gives the minimum value.
- If (the parabola opens downwards), the vertex gives the maximum value.
Would you like further explanation on this or have more questions?
Here are five related questions for practice:
- How do you find the x-coordinate of the vertex using the formula ?
- What happens to the vertex if the quadratic function is shifted vertically?
- Can the vertex ever be the x-intercept of the quadratic function?
- How does the value of affect whether the vertex is a maximum or minimum?
- How do you find the axis of symmetry from a quadratic function?
Tip: In the vertex form of a quadratic function, , the vertex is directly given as , and the y-coordinate is the maximum or minimum value.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Vertex of Parabola
Formulas
Vertex formula x = -b / (2a)
Quadratic function f(x) = ax^2 + bx + c
Theorems
Vertex theorem for parabolas
Suitable Grade Level
Grades 9-10
Related Recommendation
Finding the Minimum or Maximum Value of a Quadratic Function
Identify Maximum or Minimum Point of a Quadratic Function
Determine Minimum or Maximum Value of a Quadratic Function in Vertex Form
Determine the Minimum Value of a Quadratic Function from its Graph
Vertex and Minimum Value of Quadratic Functions