Question Find the roots and the vertex of the quadratic on a calculator. Round all values to 3 decimal places (if necessary). \[ y=20 x^{2}+180 x-567 \] Answer stamptrout of 2 Roots: \( \square \) and \( \square \)

To find the roots of the quadratic \( y = 20x^2 + 180x - 567 \), you can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Plugging in \( a = 20 \), \( b = 180 \), and \( c = -567 \), you would find the discriminant first as \( b^2 - 4ac = 180^2 - 4(20)(-567) = 32400 + 45360 = 77760 \). This provides two distinct roots when substituted back into the formula, rounded to three decimal places. To find the vertex of the parabola represented by the quadratic, you can use the vertex formula \( x = -\frac{b}{2a} \). Substituting in our values, \( x = -\frac{180}{2(20)} = -4.5 \). To find the corresponding \( y \)-value, substitute \( x = -4.5 \) back into the equation \( y = 20(-4.5)^2 + 180(-4.5) - 567 \), leading to the vertex at approximately \( (-4.5, -797.5) \) when rounded to three decimal places.