Category Archives: Grade 10

Week 8 – Precalculus 11 – Solving Quadratics Using Substitution

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My Best Mistake of the Week:

This week, my best mistake came from solving this question:

x^2 - 4x - 15 = 0

At first, I tried to factor it right away, but it didn’t factor nicely with whole numbers. I kept trying different combinations and got stuck. My factoring didn’t work, and I realized I needed a different approach.

What I learned:

After checking my notes, I remembered that some quadratics cannot be factored easily, and the quadratic formula is a reliable method for any equation:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Using the formula makes solving tricky quadratics much easier.

Correct Steps that I did:

Here, a = 1, b = -4, c = -15

Substitute into the quadratic formula:

x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-15)}}{2(1)}
x = \frac{4 \pm \sqrt{16 + 60}}{2}
x = \frac{4 \pm \sqrt{76}}{2}
x = \frac{4 \pm 2\sqrt{19}}{2}
x = 2 \pm \sqrt{19}

So the solutions are:

x = 2 + \sqrt{19} or x = 2 - \sqrt{19}

Check:

If I plug x = 2 + \sqrt{19} into the original equation:

(2 + \sqrt{19})^2 - 4(2 + \sqrt{19}) - 15 \approx 0 ✅

Reflection:

This mistake helped me see that not all quadratics can be factored easily, and the quadratic formula is very useful. Now I know that when factoring seems impossible, I should use the formula instead. It keeps my work accurate, avoids frustration, and makes solving any quadratic possible.

CBC and VFS Field Trip

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For our New Media class we went on a field trip to CBC and VFS in downtown Vancouver. The trip was a great opportunity to learn about the different things in. CBC gave us an inside look at how news is delivered to the public. I learned that CBC has multiple sections each responsible for different tasks such as control rooms and how they control camera. It was great opportunity to see how everything comes together to deliver the news. In the control room, I saw how the cameras were managed and how the team worked together to create live broadcasts. Then, we visited Vancouver Film School (VFS) where I learned about the game design and movie making. The school offers a wide range of classes including ones focused on 3D animation, game design, and writing. It was amazing to see how VFS prepares students for careers in the entertainment industry with less than a year. The locations we visited were in downtown Vancouver which was about a 50 minute drive from our school and we took the bus. The field trip was scheduled for February 21, 2025, and it was a great chance to explore these media industries in person. One of the key takeaways from the CBC was understanding the level of coordination and teamwork to produce a live broadcast. There are so many behind the scenes tasks happening that we don’t know about it and everything must be organized perfectly. The VFS taught me about entertainment industry and how many different fields you can go into from filmmaking to game development. The instructors emphasized the creative side of things showing how you can combine your passion with technical skills. I really enjoyed the field trip because I was able to see how media help the world to produce news and entertainment. It was inspiring to hear from people who work in these industries and to learn about the different career paths available. Overall I learned a lot about the importance of teamwork in media production and the opportunities that exist in the field. If it’s your first time visiting CBC or VFS, I recommend asking as many questions as you can. Every room you visit has their own purpose, and the more you understand about each task the more you’ll appreciate the work that goes into creating media.

This is a photo of me and my classmate at CBC where we’re learning about how they control the cameras. It was an exciting experience getting an inside look at the controlling cameras.