Questions: Find the coordinates of all intercepts shown in the graph to the right of the equation (y=12 x^2-11 x-5). What is/are the x -intercept(s)? Select the correct choice below and fill in any answer boxes within your choice. A. The (x)-intercept(s) is/are (square) . (Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no (x)-intercept.

$Find the coordinates of all intercepts shown in the graph to the right of the equation (y=12 x^2-11 x-5). What is/are the x -intercept(s)? Select the correct choice below and fill in any answer boxes within your choice. A. The (x)-intercept(s) is/are (square) . (Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no (x)-intercept.$

Transcript text: Find the coordinates of all intercepts shown in the graph to the right of the equation $y=12 x^{2}-11 x-5$. What is/are the x -intercept(s)? Select the correct choice below and fill in any answer boxes within your choice. A. The $x$-intercept(s) is/are $\square$ . (Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no $x$-intercept.

Solution

Solution Steps

Step 1: Finding $x$-intercepts

To find the $x$-intercepts of the quadratic equation $y=ax^2+bx+c$, we set $y=0$ and solve for $x$ using the quadratic formula: $$ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} $$ Since $b^2-4ac > 0$, there are two distinct real $x$-intercepts: x1 = 1.25, x2 = -0.33.

Step 2: Finding $y$-intercept

To find the $y$-intercept of the quadratic equation $y=ax^2+bx+c$, we set $x=0$ and solve for $y$. This gives the $y$-intercept as $(0, c)$, which is: $$y = -5$$