Question

Order each group of quadratic functions from widest to narrowest graph.
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Captionless Image
-3x², -x², -5x²
-x², -3x², -5x²
-5x², -x², -3x²

Answer 1

To determine the width of the graphs of the quadratic functions given, we look at the coefficients of \( x^2 \) in each function.

In general, for quadratic functions in the form \( ax^2 \):

1. If \( |a| < 1 \), the graph is wider.
2. If \( |a| = 1 \), the graph has a standard width.
3. If \( |a| > 1 \), the graph is narrower.

Now, let's analyze each function:

- For \( -3x^2 \), the coefficient is \( -3 \) (which gives \( |a| = 3 \)).
- For \( -x^2 \), the coefficient is \( -1 \) (which gives \( |a| = 1 \)).
- For \( -5x^2 \), the coefficient is \( -5 \) (which gives \( |a| = 5 \)).

Now, let's list them according to \( |a| \) values:

1. \( -x^2 \) (widest, \( |a| = 1 \))
2. \( -3x^2 \) (middle, \( |a| = 3 \))
3. \( -5x^2 \) (narrowest, \( |a| = 5 \))

Thus, the correct order from **widest to narrowest** is:

**-x², -3x², -5x²**.