Comparing features of functions (example 2) | Functions and their graphs | Algebra II | Khan Academy

TL;DR

Determine the maximum values of three quadratics, with h(x) = -1, g(x) = 5, and f(x) = 8, and find that h(x) has the lowest maximum value.

Transcript

Which quadratic has the lowest maximum value? So let's figure out the maximum value for each of these-- and they're defined in different ways-- and then see which one is the lowest. And I'll start with the easiest. So h of x. We can just graphically look at it, visually look at it, and say-- what's the maximum point? And the maximum point looks lik... Read More

Key Insights

• ❓ Quadratics can have different maximum values.
• 🆘 Graphical analysis can help determine the maximum value of a quadratic.
• 😑 Completing the square is a method to find the maximum value when given the expression.
• 💠 The vertex of a quadratic represents the maximum or minimum value depending on the shape of the parabola.

Questions & Answers

Q: How do you determine the maximum value of a quadratic?

To find the maximum value of a quadratic, you can graphically determine the highest point or complete the square to rewrite the quadratic in vertex form and identify the vertex as the maximum value.

Q: What is the maximum value of h(x)?

The maximum value of h(x) is -1, which occurs when x is equal to 4.

Q: What is the maximum value of g(x)?

The maximum value of g(x) is 5, which occurs when x is equal to 0.

Q: How do you find the maximum value of f(x) when given the expression?

To find the maximum value of f(x), you can complete the square by adding and subtracting a number to make part of the expression a perfect square. In the case of f(x)=-x^2+6x-1, the maximum value is 8 and occurs when x is equal to 3.

Summary & Key Takeaways

• h(x) has a maximum value of -1 when x is equal to 4.

• g(x) has a maximum value of 5 when x is equal to 0.

• f(x) has a maximum value of 8 when x is equal to 3.