Problem

Find the $x$-intercept(s) and the coordinates of the vertex for the parabola $y=x^{2}-6 x+5$. If there is more than one $x$ intercept, separate them with commas.

Solution

Step 1 :Given the parabola equation \(y=x^{2}-6 x+5\).

Step 2 :Find the x-intercepts by setting y to 0 and solving for x in the equation \(x^{2}-6 x+5=0\).

Step 3 :Use the quadratic formula \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\) to solve for x, where a = 1, b = -6, and c = 5.

Step 4 :Calculate the x-intercepts to get x1 = 5.0 and x2 = 1.0.

Step 5 :Find the vertex of the parabola using the formulas \(h = -\frac{b}{2a}\) and \(k = c - \frac{b^{2}}{4a}\).

Step 6 :Calculate the vertex to get h = 3.0 and k = -4.0.

Step 7 :Final Answer: The x-intercepts of the parabola are at \(x = 1.0\) and \(x = 5.0\). The vertex of the parabola is at the point \((3.0, -4.0)\). So, the final answer is \(\boxed{(1.0, 5.0), (3.0, -4.0)}\).

From Solvely APP
Source: https://solvelyapp.com/problems/36054/

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