Question

use your graphing calculator to sketch the graph of the function, then determine the coordinates of the x-intercepts for the function, if they exist.

$y = -2x^2 + 5x - 2$

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 parabola's direction

The function is \( y = -2x^2 + 5x - 2 \). The coefficient of \( x^2 \) is \(-2\), which is negative. So the parabola opens downward. Among the options, only option A has a downward - opening parabola (the graph in A is a downward - opening parabola, while B, D are upward - opening and C has a different shape).

Step2: Verify the x - intercepts (optional for graph selection)

To find the x - intercepts, set \( y = 0 \), so we solve the equation \(-2x^2+5x - 2=0\). Multiply both sides by \(-1\) to get \( 2x^2 - 5x + 2 = 0 \). Factor the quadratic: \( 2x^2-4x - x + 2=0\), \( 2x(x - 2)-(x - 2)=0\), \((2x - 1)(x - 2)=0\). The solutions are \( x=\frac{1}{2}\) and \( x = 2 \), which are positive x - values. The graph in option A is consistent with a downward - opening parabola with x - intercepts in the positive x - region.

Answer:

A.