2a. [2 marks] The graph of the quadratic function f(x) =...

2a. [2 marks] The graph of the quadratic function f(x) = 1/2(x - 2)(x + 8) intersects the y-axis at (0, c). Find the value of c. 2b. [2 marks] The vertex of the function is (-3, -12.5). Write down the equation for the axis of symmetry of the graph. 2c. [1 mark] The equation f(x) = 12 has two solutions. The first solution is x = -10. Use the symmetry of the graph to show that the second solution is x = 4. 2d. [2 marks] Write down the x-intercepts of the graph.

Transcript

00:01 Okay, so if we want to, i want to turn my standard form, 3x squared plus 24x plus 50, into a vertex form like this, 8 times x minus h squared plus k.

00:14 I'm going to do that by completing the square.

00:17 Okay.

00:18 So to get that, we're going to start with factoring a three out of both of these terms.

00:25 So i have x squared plus 8x.

00:29 From there, i'm going to do my process of completing the square, which is taking that 8 term, divided by 2, which is 4, and then taking 4 and squaring that.

00:39 So it gives me a plus 16 here.

00:42 Now, because i factored out the 3, and that's all inside the parentheses, i need to balance that out.

00:47 So if i have a plus 50, i also have to do a minus 48, because 48 is the same as 3 times 16.

00:53 So in this scenario, i'm adding a positive 16.

00:56 I need to balance it out by not a positive 16.

00:59 A positive 3 times 16 give me 48.

01:02 So i got to bounce out by doing a negative 48 here.

01:06 So i'll complete in the square.

01:07 I can do now as x plus 4 to the second power.

01:11 And then plus 2.

01:15 So what this tells us is the vertex is at the point that is related to 4 and 2 here.

01:21 It is at negative 4.

01:23 Oops, negative 4 positive 2.

01:27 Okay.

01:29 Let's see.

01:29 Find the vertex.

01:30 The x symmetry.

01:30 The x symmetry matches up to the x -s symmetry matches up to the x -ve.

01:32 Value there, so it's x equals negative 4, and the intercepts.

01:36 So right here, this is going to tell me one of my intercepts, which is the point 050.

01:42 So that is the y intercept for this case here.

01:45 To help with the rest of this, i'm going to solve, so we're going to take 0 is equal to 3 times x plus 4 squared plus 2.

01:56 We'll just subtract 2 over.

01:59 So negative 2 is equal to 3 times x plus 4 squared.

02:04 Then we get divided by 3, negative 2 thirds is equal to x plus 4 squared.

02:12 So now here's my problem.

02:13 If i try to square root this, now i'm square reading negative, and that's not realistic.

02:18 So all i have for intercepts is just going to be the y intercept, which is the plus 50 here.

02:23 So that's going to be at 0 .50.

02:29 For the next problem, we want to look like we're doing a piecewise function is what it looks like to me on here...

Question

Please give Ace some feedback