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2x^(2)-6x=-4 Vertex: ) x y Solution:

2x2−6x=−4 2 x^{2}-6 x=-4 \newlineVertex:\newline)\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline & \\\newline\hline & \\\newline\hline & \\\newline\hline & \\\newline\hline & \\\newline\hline\newline\end{tabular}\newlineSolution:

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Q. 2x2−6x=−4 2 x^{2}-6 x=-4 \newlineVertex:\newline)\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline & \\\newline\hline & \\\newline\hline & \\\newline\hline & \\\newline\hline & \\\newline\hline\newline\end{tabular}\newlineSolution:
  1. Rewrite Equation in Standard Form: Rewrite the equation in standard form.\newlineTo find the vertex of a parabola, we need the quadratic equation in the form of ax2+bx+c=0ax^2 + bx + c = 0. Let's add 44 to both sides of the equation to get it in standard form.\newline2x2−6x+4=02x^2 - 6x + 4 = 0
  2. Identify Coefficients: Identify the coefficients aa, bb, and cc. In the standard form ax2+bx+c=0ax^2 + bx + c = 0, the coefficients are: a=2a = 2, b=−6b = -6, c=4c = 4
  3. Use Vertex Formula: Use the vertex formula.\newlineThe vertex of a parabola given by ax2+bx+cax^2 + bx + c is at the point (h,k)(h, k), where h=−b2ah = -\frac{b}{2a}. Let's calculate hh.\newlineh=−(−6)2⋅2=64=1.5h = -\frac{(-6)}{2\cdot 2} = \frac{6}{4} = 1.5
  4. Calculate Y-Coordinate: Calculate the y-coordinate of the vertex.\newlineTo find the y-coordinate kk of the vertex, we substitute x=hx = h into the original equation.\newlinek=2(1.5)2−6(1.5)+4k = 2(1.5)^2 - 6(1.5) + 4\newlinek=2(2.25)−9+4k = 2(2.25) - 9 + 4\newlinek=4.5−9+4k = 4.5 - 9 + 4\newlinek=−0.5k = -0.5
  5. Write the Vertex: Write the vertex.\newlineThe vertex of the parabola is at the point (h,k)(h, k), which is (1.5,−0.5)(1.5, -0.5).

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