Questions: An equation is given: y = √x^2 + 4x + (-2.21)y + 4.1) Use a graphing calculator to graph the equation in the given viewing rectangle. y intercept (x, y) = x intercept (x, y) = x intercept (x, y) = Find the x- and y-intercepts from the graph. Verify your answers algebraically (from the equation). *If an answer does not exist, enter DNE.

An equation is given: y = √x^2 + 4x + (-2.21)y + 4.1)

Use a graphing calculator to graph the equation in the given viewing rectangle.

y intercept (x, y) =
x intercept (x, y) =
x intercept (x, y) =

Find the x- and y-intercepts from the graph. Verify your answers algebraically (from the equation). *If an answer does not exist, enter DNE.

Transcript text: An equation is given: y = √x^2 + 4x + (-2.21)y + 4.1) Use a graphing calculator to graph the equation in the given viewing rectangle. y intercept (x, y) = x intercept (x, y) = x intercept (x, y) = Find the x- and y-intercepts from the graph. Verify your answers algebraically (from the equation). *If an answer does not exist, enter DNE.

Solution

Solution Steps

Step 1: Find the x-intercepts from the graph

The graph intersects the x-axis at x=0 and x=1. Therefore, the x-intercepts are (0,0) and (1,0).

Step 2: Verify the x-intercepts algebraically

To verify the x-intercepts algebraically, we set y=0 in the equation y = x³ - x² and solve for x. 0 = x³ - x² 0 = x²(x - 1) x² = 0 or x - 1 = 0 x = 0 or x = 1 Thus, the x-intercepts are (0, 0) and (1, 0).

Step 3: Find the y-intercept from the graph

The graph intersects the y-axis at y=0. Therefore, the y-intercept is (0,0).