MathGrade 9ages 14–15
〰️ A parabola
The graph of x squared curves into a bowl shape, not a straight line — and a single minus sign in front of the square is enough to flip that bowl into a dome.
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- A number squared is always positive or zero.
- So both sides of the graph climb by the same amount, and the shape comes out symmetric.
- With no minus sign the parabola opens upward like a bowl.
- A minus sign flips every height, which turns the bowl into a dome.
The mistake most kids make here
Thinking the graph of a square is a straight line.
Try one question
The graph of x squared. Which way does it open?
x squared
- upward
- downward
- it is a straight line
Answer
upward — That's it. A bowl whose bottom sits at the origin.
How Maya teaches it
Your child tells Maya what they did in class. She teaches this topic at her desk, asks questions with tappable answers, and when the answer is wrong she explains why that answer was tempting instead of saying “try again”. She remembers what did not land and comes back to it.
Your child has it when they can: Say which way a parabola with a minus sign opens.
How to help at home
Squaring a number always gives a positive result (or zero), whether the number itself was positive or negative. That's the whole reason the graph curves symmetrically upward on both sides instead of running in a straight line.
Make a small table together: x = -2, -1, 0, 1, 2, and y = x². Plot the points on graph paper or even a napkin grid. Watch the shape emerge as a symmetric bowl, lowest at x = 0.
When your child expects a straight line (because most graphs they've seen so far are lines), point to the table: "both -2 and 2 give the same y value, 4. A straight line couldn't do that — only a curve that comes back down on the other side."
A sign they've got it: shown y = -x², they can predict the bowl flips into a dome before plotting a single point, because they know the minus sign flips every height.
Questions parents ask
- Why is the graph of x squared a curve and not a line?
- Because squaring treats -2 and 2 the same way (both give 4), the graph has to rise on both sides of zero and come back down symmetrically — a shape a straight line can't make.
- How does a minus sign change the parabola's shape?
- A minus sign flips every y-value from positive to negative (or the reverse), which turns an upward-opening bowl into a downward-opening dome, with the same symmetric shape.
- What's the lowest or highest point of a parabola called?
- It's called the vertex — the bottom of a bowl-shaped parabola, or the top of a dome-shaped one.
- How does Maya teach parabola shapes?
- Maya has the child build a table of values and plot points by hand before naming the shape, so the curve comes from evidence rather than a memorized rule.
No card needed. The first lesson is free.
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