Evaluate the function k(x) = -3x^2 + 6 at two different...

Evaluate the function $k(x) = -3x^2 + 6$ at two different inputs and state the corresponding points. k( ) = , which corresponds to the point . k( ) = , which corresponds to the point .

Transcript

00:01 So for this problem, we're given two points.

00:03 We have negative 3, comma, 2, and then 0, 11.

00:16 And we have to determine what the a and k value are in the equation y is equal to a times x plus 2 squared plus k, so that both points are on.

00:49 The graph of the function.

00:52 So to start off, i'm going to label each of the point.

00:57 So we have x, y, x, y, x, y, and i'm going to substitute or plug in each point into the equation.

01:09 So starting with negative three comma two, we have two is equal to.

01:15 We don't know what a is, so a times negative 3 plus 2 squared plus k so then according to order of operations we have to do whatever is in the parentheses first so we have a times negative 3 plus 2 is negative 1 squared plus k then negative 1 square which is the same thing as 2 2 2 times negative 1 is just 1 so we have 1 a plus k so that's all we can simplify for now.

01:56 Then for the point zero come 11 we're going to plug that into the equation.

02:00 We have 11 is equal to a times zero plus two squared plus k.

02:19 We have 11 is equal to a times zero plus 2.

02:27 So we have 2 squared plus k.

02:34 2 square is the same thing as 2 times 2, which is 4.

02:38 So we have 4 times a plus k.

02:45 So now that we have these two equations, we are going to solve for a by subtracting the two equations.

03:00 So this is one way to solve a system of equations by elimination.

03:06 So we we're eliminating the k to solve for a and then we'll go back to trying to find the k value so i wrote the two equations one on top of the other and so if we subtract the equations from each other k minus k number minus itself will always be zero so that crosses out then we have 11 minus two which is nine and then for a minus three one a is three a and then to solve for what a is a is and then to solve for what a is we have to get the three to the other side, so we have to do the opposite or the inverse operation.

03:44 So the opposite of multiplying by three is dividing by three.

03:47 So we have three divided by three, which is just one, so we're left with a is equal to, and then nine divided by three is three.

03:55 So we found our a value, and to find our k value, we're going to substitute a into the equation, and i'm going to choose the point zero comma 11 to substitute as well.

04:08 So we have y is equal to a is three.

04:16 Then i'm going to just rewrite the equation with our a value...

Question

Evaluate the function $k(x) = -3x^2 + 6$ at two different inputs and state the corresponding points. k( ) = , which corresponds to the point . k( ) = , which corresponds to the point .

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