Question

use your graphing calculator to sketch the graph of the function, then determine the domain and range of the function.
$y = -5x^2 + 6x - 1$

graph the function using a graphing calculator.
\\(\bigcirc\\) a.
\\(\bigcirc\\) b.
\\(\bigcirc\\) c.
\\(\bigcirc\\) d.

–10,10 by –20,20,
xscl=1, yscl=2
–10,10 by –20,20,
xscl=1, yscl=2
–10,10 by –20,20,
xscl=1, yscl=2
–10,10 by –20,20,
xscl=1, yscl=2

Explanation:

Step1: Analyze the coefficient of \(x^{2}\)

For the quadratic function \(y = ax^{2}+bx + c\), the coefficient of \(x^{2}\) (i.e., \(a\)) determines the direction the parabola opens. In the function \(y=- 5x^{2}+6x - 1\), \(a=-5\). Since \(a=-5<0\), the parabola opens downward.

Step2: Identify the correct graph

Among the given graph options, the graphs in options B and C have upward - opening parabolas (since they open upwards, which would correspond to \(a > 0\)), and the graph in option D seems to be a narrower or incorrectly shaped parabola for this function. The graph in option A has a downward - opening parabola, which matches the sign of \(a=-5\) in our quadratic function.

Answer:

A. The graph with the downward - opening parabola (the first graph option)