Does the parable
Is there a minimum or maximum point?
We have hundreds of course questions with personalized recommendations + Account 100% premium
Does the parable
Is there a minimum or maximum point?
To determine whether the quadratic function has a minimum or maximum point, we need to examine its structure and calculate the vertex.
Step 1: Identify the structure of the quadratic function.
The given function is , which is a standard form quadratic function where , , and .
Step 2: Calculate the vertex.
The vertex of a quadratic function is given by . Substituting the values of and into this formula gives:
.
Substitute back into the original equation to find the y-coordinate of the vertex:
.
Therefore, the vertex is at the point .
Step 3: Determine if the vertex is a minimum or maximum.
Since the coefficient is positive, the parabola opens upwards. This means that the vertex represents the lowest point on the graph, which is a minimum point.
Therefore, the solution to this problem is that the parabola has a minimal point.
Minimal point
What is the value of the coefficient \( b \) in the equation below?
\( 3x^2+8x-5 \)
Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime