Several graphs of the quadratic function ƒ(x) = ax^2 + bx + c are...

Question

Several graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) A > 0; b^2 - 4ac > 0

Accepted Answer

Hey, everyone in this problem, we're asked which of the following graphs of a quadratic function satisfies the condition given below the condition we're given is that A is greater than zero and B squared minus four AC is greater than zero. We have four answer choices. Each of them is a graph option A is a quadratic function. It opens upwards and it has two zeros. Option B is a quadratic function that opens upwards but does not have any zeros A or X intercepts. Option C and D both open downwards. Option C has no X intercepts and option D has one X intercept. So let's go back to the conditions we were given. So let's write the general equation for a quadratic function we have that Y is equal to A X squared plus B X plus C. In standard form, starting with the first piece of information we're given A is greater than zero. If the leading coefficient is positive, it tells us that our parabola opens upward. OK. So we know that we're looking at answer choice either A or B. Now when we're giving B squared minus four AC, we're call that that's the discriminate. And in order to see what a negative or sorry, a positive discriminant gives us, let's recall the quadratic formula. If we want to find the X intercepts of our function Y, we can write that they are equal to X equals negative B plus or minus the square root of B squared minus four AC all over two A. So we can see that this discriminate B squared minus four AC is the portion that's under the square root. So if that is positive, it tells us that we are going to have two real roos. Why is that? Well, when we take the square root of a positive number, we're gonna get a value. And then our equation for the X intercept gives us plus or minus that value. OK? So that's gonna give us two different answers when we add the value versus when we subtract the value. OK. So if the discriminates positive, we get two real roots. So now we know that we have a Parabola that opens upwards and has two rail routes. And so this corresponds with answer choice A, that graph of the Parabola opening upwards with two X intercepts. That's it for this one. Thanks everyone for watching. I hope this video helped.

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Several graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) A > 0; b^2 - 4ac > 0