Comparing features of quadratic functions | Mathematics II | High School Math | Khan Academy

TL;DR

Determine which function has a greater y-intercept, find the number of roots they have in common, and determine if the functions have the same concavity.

Transcript

• [Voiceover] So we're asked which function has the greater y-intercept? So, the y-intercept is the y-coordinate when x is equal to zero. So, f of zero, when x is equal to zero, the function is equal to, let's see, f of zero is going to be equal to zero minus zero, plus four, is going to be equal to four. So this function right over here, it has a ... Read More

Key Insights

• ❣️ The y-intercept of a function is the y-coordinate when x is equal to zero.
• 😀 Function f(x) has a greater y-intercept compared to function g(x).
• 🫚 The number of roots in common between two functions can be determined by finding their shared zeros.
• ☺️ Concavity of a function is determined by the coefficient on the x squared term.
• 📈 Function f(x) is concave upwards, while function g(x) is concave downwards.
• 📈 The concavity of a function affects the shape of its graph.
• ☺️ Function f(x) has roots at x = -3 and x = 2.

Questions & Answers

Q: Which function has a greater y-intercept?

Function f(x) has a y-intercept of 4, while function g(x) has a y-intercept of 3.

Q: How many roots do the functions have in common?

Both functions have one root in common, which is x = 2.

Q: What is concavity and do the functions have the same concavity?

Concavity refers to whether a graph opens upwards or downwards. The coefficient of the x squared term determines the concavity. Function f(x) is concave upwards, while function g(x) is concave downwards. They do not have the same concavity.

Q: How can we determine the roots of function f(x)?

To find the roots of function f(x), we can factor the equation. By factoring x^2 + x - 6, we find that f(x) has zeros at x = -3 and x = 2.

Summary & Key Takeaways

• The y-intercept of function f(x) is 4, while the y-intercept of function g(x) is 3.

• Both functions have one root in common, which is x = 2.

• Function f(x) is concave upwards, while function g(x) is concave downwards.