If the discriminant is positive, the distance would be non-zero, and there will be two solutions. This is one of three cases, where the discriminant indicates how many zeros the parabola will have. Algebraically, this means that √ b 2 − 4 ac = 0, or simply b 2 − 4 ac = 0 (where the left-hand side is referred to as the discriminant). If this distance term were to decrease to zero, the value of the axis of symmetry would be the x value of the only zero, that is, there is only one possible solution to the quadratic equation.
#Standard form of quadratic equation plus
The other term, √ b 2 − 4 ac / 2 a, gives the distance the zeros are away from the axis of symmetry, where the plus sign represents the distance to the right, and the minus sign represents the distance to the left. The axis of symmetry appears as the line x = − b / 2 a. And we got it right.X 1 = − b + b 2 − 4 a c 2 a or x 2 = − b − b 2 − 4 a c 2 a So first I'll do the vertexĪt 2 comma negative 5, which is right there. Which is equal to- let's see, this is equal to 2 squared is 4. When x equals 2, y is going toīe equal to 5 times 2 squared minus 20 times 2 plus 15, To substitute back in to figure out its y-coordinate. Sits exactly smack dab between the roots, I want to figure out, is this point right This is true, and you canĪdd 3 to both sides of this. And so this will be true ifĮither one of these is 0. X's will make this expression 0, and if they make Side, we still have that being equal to 0. On factoring quadratics if this is not so fresh- isĪ negative 3 and negative 1 seem to work. And whose sum is negativeĤ, which tells you well they both must be negative. Whose product is positive 3? The fact that their And now we can attempt toįactor this left-hand side.
Plus 15 over 5 is 3 isĮqual to 0 over 5 is just 0.
Me- these cancel out and I'm left with x squared The x squared term that's not a 1, is to see if I canĭivide everything by that term to try to simplify I like to do whenever I see a coefficient out here on We're going to try to solve the equation 5x Those three points then I should be all set with And then I also want toįigure out the point exactly in between, which is the vertex. Minus 20x plus 15, when does this equal 0? So I want to figure Seen, intersecting the x-axis is the same thingĪs saying when it does this when does y equal I want to first figure out whereĭoes this parabola intersect the x-axis. You can just take threeĬorresponding values for y are and just graph
The following equation y equals 5x squared Therefore, 3 and 1 are the only possible x values. So -3 doesn't work as an x, and the same thing would happen with -1:īoth of these solved binomial equations show that -3 and -1 cannot be x values for the parabola. X cannot equal -3 or -1 because if x was -3 then this would happen: The reason that Sal made the x values positive 3 and 1 is because they are the only two x values that would make his equation equal zero.
#Standard form of quadratic equation how to
(this basically explains how to get the 3 and 1 for the x values and it explains why -3 and -1 do not work for x values.) I think that was the question you were asking, I hope that helped, if not, hopefully this will: you can check them out if you are still confused. The -3 and -1 were not x values, they were just what he used to factor in a way that he teaches in previous factoring videos. In order to find the x values he used that binomial and made it equal 0, and his x values that he found were 3 and 1. the -3 and -1 were numbers that he got when he factored the equation into a binomial.
the -3 and the -1 that he got were not his x values. He didn't exactly switch his x values to positive.
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