This is really helpful! It’s so easy to zone out when my teacher is explaining stuff- she talks about really random stuff building up, and won’t get to the point for a while
I have three kids doing Junior High and High School math remotely. I watch a lot of math videos with varying degrees of complexity. This one seems a trifle challenging, particularly in the way he works so quickly. I'll file this video for future use when my Algebra skills are a bit stronger. Having said that, there's some valuable info in this video.
Thanks, man. Solid teaching. Just a question if you are able to answer it. Why does equation 2 and 3 given at the start always show in brackets (X - constant), why is it always minus and never plus? I think I may know the answer intuitively it looks like it's related to transformations, i.e. when you move a graph in the X direction by amount '+d', the equation changes by (X-d) and so on. Think I may have answered my own question typing my thoughts lol, but some confirmation/guidance would be extremely useful. Thanks dude and great video!
Go to 4:46 in the video. This example has the vertex and the y-intercepts. With x-intercepts you do the same thing; just choose one of the x-intercepts and sub it in the equation to solve for a.
Find the x value of the maximim/minimum by x = -b/2a (or half way between the 2 roits) and then put that value back into the original y=,,, or f(x) =,,,,, equation
As long as they give you one put on the graph, you can still substitute in these values for x and y into your equation. This will enable you to work out the value of a, the leading coefficient.
What if i just have the graph and the (h, k)? WHat other info can I pull of the graph? My y intercept is a repeating decimal. Same with my p and q. I have AN equation, but it isnt in any proper form, and i cant fix it. 12y=(x-1)^2 -48. Its in the one form but with the extra number on the side. what should i do? I need to find my focus and directrix for my question.
You can rewrite the equation as y = 1/12 (x - 1)^2 - 4 , by dividing both sides by 12. If you make x = 0, you will find that the y-intercept will be 1/12 - 4 = - 3.9166667 or -3 11/12. To find the focus and directrix you need to rewrite your equation in the form 4p(y - k) = (x - h)^2, which in this case will be 12 (y + 4) = (x - 1)^2 . (h, k) is still the vertex, so in this case the vertex is (1, -4). The parameter p is called the focal length, so in this case p = 12/4 = 3. Therefore, the focus is (1, -1), which is 3 up from the vertex, and the directrix is y = -7, which is 3 down from the vertex. The focus / directrix question is really different from the usual equation of a parabola questions. I suggest searching for another video to get in more depth for this, or if you just need the answer for one question use a calculator like the one on this site, www.symbolab.com/solver/parabola-directrix-calculator/.
In the equation y = a (x - p) (x - q) , you can replace p and q with the x-intercepts. But you will still have an equation that relates x to y. For example, if your equation is y = (x -2)(x - 1), you can rearrange that to y = x^2 - 3x + 2, so any point (x, y) on the graph will satisfy this equation, i.e. make the equation true. I hope this answers your question.
The value of b is a little harder to understand than the other letters. If b is negative, it means the vertex of the graph will be on the positive side (i.e. right of the y-axis); if b is positive, it means the vertex is on the left of the y-axis. But, it is probably more useful just to remember that the vertex is where x = -b/(2a). This is why it is useful to rewrite the equation in different formats; because the different formats give you different information.
If the question doesn't give you one of the specific points (like c, or p or q or h or k), but they do give you another point, you can sub the x and y values from that point into your equation and solve for c. The whole principle is, there are three unknowns, a, b and c. So we need three points to solve for them, unless they give us a special point like the vertex. Good luck.
