The quadratic function with the narrowest graph is determined by the absolute value of the coefficient of \( x^2 \) (also known as the "leading coefficient"). The larger the absolute value of this coefficient, the narrower the graph.
Let's compare the given functions:
1. \( y = -2x^2 \): Here, the leading coefficient is -2. The absolute value is |−2| = 2.
2. \( y = -3x^2 \): Here, the leading coefficient is -3. The absolute value is |−3| = 3.
Since 3 is greater than 2, the quadratic function \( y = -3x^2 \) has the larger absolute leading coefficient, and therefore it has the narrowest graph.
**So, \( y = -3x^2 \) has the narrowest graph.**
4.
Which of the quadratic functions has the narrowest graph?
y = −2x2
y = −3x2
1 answer