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Use the ALEKS graphing calculator to find the vertex and x-intercept(s) for the quadratic function. f(x)=-3x^(2)-11 x-5 Round to the nearest hundredth if necessary. If there is more than one x-intercept, separate them with commas. If applicable, click on "None".

Use the ALEKS graphing calculator to find the vertex and x x -intercept(s) for the quadratic function.\newlinef(x)=−3x2−11x−5 f(x)=-3 x^{2}-11 x-5 \newlineRound to the nearest hundredth if necessary.\newlineIf there is more than one x x -intercept, separate them with commas.\newlineIf applicable, click on

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Q. Use the ALEKS graphing calculator to find the vertex and x x -intercept(s) for the quadratic function.\newlinef(x)=−3x2−11x−5 f(x)=-3 x^{2}-11 x-5 \newlineRound to the nearest hundredth if necessary.\newlineIf there is more than one x x -intercept, separate them with commas.\newlineIf applicable, click on
  1. Identify General Form and Coefficients: Identify the general form of the quadratic equation and the coefficients for calculation.\newlineGiven f(x)=−3x2−11x−5f(x) = -3x^2 - 11x - 5, the coefficients are a=−3a = -3, b=−11b = -11, and c=−5c = -5.
  2. Calculate Vertex: Calculate the vertex using the formula for the x-coordinate of the vertex, x=−b2ax = \frac{-b}{2a}.x=−(−11)2∗(−3)=116≈1.83x = \frac{-(-11)}{2*(-3)} = \frac{11}{6} \approx 1.83
  3. Substitute for Y-Coordinate: Substitute xx back into the function to find the yy-coordinate of the vertex.\newliney=−3(1.83)2−11(1.83)−5≈−28.07y = -3(1.83)^2 - 11(1.83) - 5 \approx -28.07\newlineVertex is approximately (1.83,−28.07)(1.83, -28.07).
  4. Find X-Intercepts: Find the x-intercepts using the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineDiscriminant = (−11(-11^22 - 44*(−3-3)*(−5-5) = 121121 - 6060 = 6161\newlinexx-intercepts: x=−(−11)±612∗(−3)x = \frac{-(-11) \pm \sqrt{61}}{2*(-3)}\newlinex1=11+61−6≈−0.92x_1 = \frac{11 + \sqrt{61}}{-6} \approx -0.92, x2=11−61−6≈−2.75x_2 = \frac{11 - \sqrt{61}}{-6} \approx -2.75

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