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Use the ALEKS graphing calculator to find the x-intercept(s) and vertex for the quadratic function. f(x)=2x^(2)-x+2 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 x x -intercept(s) and vertex for the quadratic function.\newlinef(x)=2x2−x+2 f(x)=2 x^{2}-x+2 \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 x x -intercept(s) and vertex for the quadratic function.\newlinef(x)=2x2−x+2 f(x)=2 x^{2}-x+2 \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 Quadratic Formula: Identify the quadratic formula and coefficients.\newlineThe quadratic function given is f(x)=2x2−x+2f(x) = 2x^2 - x + 2. Here, a=2a = 2, b=−1b = -1, and c=2c = 2.
  2. Calculate Vertex: Calculate the vertex using the formula for the vertex of a parabola, (h,k)(h, k) where h=−b2ah = -\frac{b}{2a} and k=f(h)k = f(h).h=−−12⋅2=14h = -\frac{-1}{2\cdot 2} = \frac{1}{4}k=2⋅(14)2−(14)+2=2⋅(116)−14+2=18−14+2=1.875k = 2\cdot\left(\frac{1}{4}\right)^2 - \left(\frac{1}{4}\right) + 2 = 2\cdot\left(\frac{1}{16}\right) - \frac{1}{4} + 2 = \frac{1}{8} - \frac{1}{4} + 2 = 1.875Vertex: (0.25,1.875)(0.25, 1.875)
  3. Find X-Intercepts: Find the x-intercepts using the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.Discriminant=(−1)2−4⋅2⋅2=1−16=−15\text{Discriminant} = (-1)^2 - 4\cdot 2\cdot 2 = 1 - 16 = -15Since the discriminant is negative, there are no real x-intercepts.

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