Quadratics in standard form basic

​Escape the Room
Quadratics in standard form Review

By Mirel Mincer - This was made with magic school ai

​Welcome, Detective! Professor Parabola, the world's leading expert on quadratic functions, has mysteriously vanished from his laboratory. His research on graphing quadratic functions in standard form was nearly complete, but now all his work has been scattered and hidden throughout his office.


Your mission: Follow the clues he left behind to piece together his research and discover what happened to him. Each clue will test your knowledge of graphing quadratic functions in standard form f(x)=ax^2+bx+c.

​🔍 THE SCENE: : You enter Professor Parabola's cluttered office. Papers are everywhere, and there's a note on his desk that reads:

​🔎 CLUE #1: On the professor's whiteboard, you find this riddle written in his handwriting

Open Ended

I'm the letter that tells you which way I go,
If I'm positive, upward I'll grow.
If I'm negative, downward I'll fall,
In standard form, I'm the first of them all.
What am I?

What's the answer detective?

​You're absolutely right! The coefficient a in f(x)=ax^2+bx+c determines the direction of the parabola's opening.
As you solve the first clue, you notice a hidden compartment in the whiteboard opens up, revealing another piece of the puzzle!

​🔎 CLUE #2: Inside the compartment, you find a crumpled piece of paper with this mathematical rap written on it:

Open Ended

🎵 "Yo, listen up, here's what you need to know,
When graphing parabolas, there's a special point to show,
It's the highest or lowest, depending on 'a',
If 'a' is positive, it's the minimum, hooray!
If 'a' is negative, it's the maximum you see,
This special point has a name, what could it be?" 🎵

The professor seems to have been working on finding this special point. What is this point called, Detective?

​As you say "vertex," a secret drawer in the professor's desk clicks open. Inside, you find a peculiar calculator with a sticky note attached...

​🔎 CLUE #3: The sticky note reads:

​As you complete the formula, the calculator's screen lights up and displays a new message... 🔎 CLUE #4: The calculator screen shows:

Open Ended

find the vertex for f(x)=2x^2-8x+3

​The vertex is indeed (2, -5)!
The calculator beeps approvingly, and suddenly a hidden panel in the wall slides open, revealing a secret passage with another clue...

​🔎 CLUE #5: In the secret passage, you find a mirror with equations written backwards on it. When you look at the reflection, you can read:

Open Ended

Detective, the y-intercept holds a special secret in standard form. When x equals zero, what remains is the key to understanding where my parabola crosses the y-axis.

For any quadratic , what is the y-intercept?

"This value appears directly in standard form!"

​As you speak the answer, the mirror rotates, revealing a hidden laboratory behind it. You step through and find Professor Parabola's main research station...

​🔎 CLUE #6: On the research table, you discover a half-finished graph with a note:

Open Ended

What do we call the values of x that make f(x)=0?

​As you say "roots," a secret door opens with a soft click. You follow the light into Professor Parabola's private study...

​🔎 CLUE #7: In the private study, you find a large poster on the wall with this message:

Open Ended

What is the equation of the axis of symmetry, Detective?

​As you solve this clue, the poster slides up, revealing a window that looks out into a garden. But wait - there's something written in the condensation on the glass...

​"Detective, I was studying how the coefficient 'a' affects the shape of my parabolas. I noticed that when |a| is large, something happens to the width, and when |a| is small, the opposite occurs." "When |a| is large (like a = 5), the parabola becomes ______." "When |a| is small (like a = 0.2), the parabola becomes ______."

​As you wipe away the condensation to reveal your answer... you find Professor Parabola sitting at a desk, perfectly fine! He looks up and smiles.

"Ah, Detective! I've been waiting for someone skilled enough to solve all my clues. I wasn't missing - I was testing whether someone truly understood quadratic functions well enough to find me!"