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 less than zero and B squared minus four AC is equal to zero. We're given four answer choices. All of them graphs. Option A and B show a quadratic or a parabola that opens upwards. The graph in option A has two X intercepts. And then B we have no X intercepts. Option C and D show Parabolas opening downwards. Option C has no X intercept and option D has one X intercept gonna go back to our conditions. And let's start by writing out what the general equation for quadratic function looks like in standard form, we have the Y is equal to A X squared plus B X plus C. Now we're told that A is less than zero. OK? If A is less than zero A is our leading coefficient, which tells us that the Parabola opens downwards. OK. So we know that we're looking at option either C or D A and be open upwards. And so those two options are out. Now we're given B squared minus four AC recall that that is the discriminate. And where does that come from? Well, if we want to solve for the X intercepts or the roots of our equation, why equals A X squared plus B X plus C? We call that we have the quadratic formula which tells us that X is equal to negative B plus or minus the square root of B squared minus four AC over two A. And so this B squared minus four AC, OK is underneath the square root in our quadratic formula. OK. And that is called the discriminate. Now, if that is equal to zero, what happens to the root? OK. Well, we have the square root of zero, which is just going to give us a zero. So when we calculate X, we have negative B plus or minus zero, whether we add zero or subtract zero, we get just negative B in the numerate. And so we're only going to get one value for X, OK. We only have one solution for X, which means that we only have one X intercept. OK. So because B squared minus four AC is equal to zero, we only get one root or one X intercept. So now we know that this parabola opens downwards and it has one root and we've already eliminated answer choice A and B, we can go and look at option C and D and we see that this corresponds with answer choice D, the Parabola opening downwards with one root. Thanks everyone for watching. I hope this video helped see you in the next one.

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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