1. For any quadratic of the form y= ax^2 + c, the axis of...

1. For any quadratic of the form y= ax^2 + c, the axis of symmetry is always (a)__________ and if the axis of symmetry is X=2, and (-1, 3) is on the graph, then the point (___, ___) must also be on the graph 2. The graph of y = 2t^2 + 4t + 3 passes through the point (1,___) and (-1, ___) 3. For the quadratic equation, y= x^2 - 4x + 8. Graph and label the following (a) Axis of symmetry. (b) Vertex

Transcript

00:01 So number one, we're being asked to fill in the blanks.

00:02 So we're given this equation, y equals a x squared plus c, where a and c are just constants, and we're told the axis of symmetry is always going to be a link.

00:12 So in this particular case, remember, our parabola, typically it has its vertex at the origin, and its axis of symmetry in this case would be the y -axis.

00:21 Well, by adding a value for c, it's either going to shift this graph up or down, depending on if c is positive or negative.

00:26 But that means the axis of symmetry would still be the y -axis.

00:30 So the fill in the first blank, the axis symmetry, would be the y -axis.

00:35 So then it says if the axis symmetry is x equals 2 and the order of pair negative 1 -3 is on the graph, whatever point is on the graph.

00:43 Okay, well, let's set up a different graph in this case.

00:45 So if we're told that our here's our y -axis and here's our x -axis, so if we're told that the axis symmetry is x -equals 2, that means we'd slide over two units to the right.

00:55 So that would mean this is where our graph is going to cut our paraboh and half.

01:00 So let's just say our graph looks something like this.

01:05 Now, they're telling us that the point negative one, three is on the graph.

01:09 So 1, 2, 3, so negative 1, 3.

01:12 Now, keep in mind that if the x equal line, x equals 2 is our x is symmetry, that means any point equidistant is going to have the same y value.

01:22 Well, negative 1 is 1, 2, 3 units to the left.

01:25 So we go 3 units to the right, so 3, 4, when x is equal to 5, it will have the same y value of 3.

01:31 So we would know the order pair 5, 3 would be on the ground.

01:34 So that's how we'll float in the second blade.

01:36 It would be the ordered pair 53.

01:38 So that's the answer to number 1.

01:40 Now, number 2 says we're given this equation, y equals 2 squared plus 14 plus 3.

01:47 And we want to fill in the blanks from the missing ordered pairs.

01:50 So it says it passes through the point 1 blank.

01:53 All right.

01:54 Well, that would mean 1 would be the t value.

01:56 We just need to find the y value.

01:57 So all we're going to do is substituting 1 for t.

02:00 So we're going to have y equals 2 times 1 squared plus 4 times 1 plus 3.

02:06 Well, 1 squared is equal to 1 times 2.

02:09 4 times 1 is 4.

02:11 So now we'll add 2 plus 4 is 6 plus 3 is 9.

02:14 So we know the order of pair 1 9 is on the graph.

02:17 Well, they also want us to figure out for the point negative 1 blank.

02:20 So this time we're just substituting in negative 1 for t...

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