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### Course: Algebra 1>Unit 14

Lesson 12: Comparing quadratic functions

# Comparing features of quadratic functions

Sal compares the y-intercepts, the zeros, and the concavity of quadratic functions given graphically and algebraically.

## Want to join the conversation?

• I can't understand how the coeficient of x square terme tell's us wether the vertex is minimum or maximum!
• If the coefficient is a positive number (2x²) the vertex will be a minimum point (the parabola will be in the shape of a "U"). The vertex is a low as your parabola will go.

if the coefficient is a negative number (-2x²), the vertex will be a maximum point (the parabola will be in a shape like "∩"). Which means the vertex is as high as your parabola will go.
• At , how did you determine that the y intercept for y=g(x) was 3. I understand how you found it for the first equation because the y intercept was 4, but how did you find it for g(x)?
• You look for the point on the y-axis that is (0, #). for that one it happened to be 3
• So concavity is either something two functions do or don't have in common, not something they can have more or less of?
Sort of like how two lines either are or aren't parallel?
• This is correct (to a degree), concavity describes the open up/down nature of the graph of a function. Later on in mathematics (Algebra 2 and beyond), concavity can identify if there's a minimum or maximum.
• I thought the opposite of concave was convex; NO?
• You are correct, considering mathematical functions, if you put a negative sign in front of a convex function, this function becomes the concave version as it is reflected across the x-axis.
• Why is it we can simplify the equation by dividing by two to make it easier to find its x's but we cannot leave it at the simplified version to find our y intercept? I thought manipulation keeps the formula the same
(1 vote)
• I could not find where in the video you are talking about, but your final statement is true if you manipulate the equation correctly, it is just a different form, but same equation. I do not know what you consider the simplified version, so could you provide an example where you cannot find the y intercept?
If you have f(x) = 2x^2 + 6x - 8 you see y int of - 8, if you take out 2 and factor, you end up with f(x) = 2(x^2 +3x - 4) = 2(x + 4)(x - 1) so if x=0, y int is 2(4)(-1) which still gives -8 and x intercepts are -4 and 1.
• Interesting! Now I know why the parabola opens up or down based on the coefficient. Algebra!
• There is another way to it also that is discriminant also determines the number of solutions a Quadratic Equation have, Right?
(1 vote)
• Yes, the discriminant can be used to determine the number of roots and what type they are. If you need their actual values, then you will need to do the complete solution.
• what does Sal mean when when he says “as x gets further and further away from the vertex”?
• As an example, let's say that the vertex is at (3,4) The xs on both sides (2,)(4,) will be relatively close to the vertex, two values away (1,)(5,) will be a little further away, but as x gets 10 or 15 units from the vertex (farther and farther away) the y values really zoom up.