Question

question
find the coordinates of the vertex of the following parabola algebraically. write your answer point.

$y = x^2 - 10x + 34$

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function in the form \( y = ax^2+bx + c \), the x - coordinate of the vertex is given by \( x=-\frac{b}{2a} \). In the equation \( y=x^{2}-10x + 34 \), we have \( a = 1 \), \( b=- 10 \) and \( c = 34 \).

Step2: Calculate x - coordinate of vertex

Substitute \( a = 1 \) and \( b=-10 \) into the formula \( x =-\frac{b}{2a} \). We get \( x=-\frac{-10}{2\times1}=\frac{10}{2} = 5 \).

Step3: Calculate y - coordinate of vertex

Substitute \( x = 5 \) into the equation \( y=x^{2}-10x + 34 \). So \( y=(5)^{2}-10\times5 + 34=25-50 + 34=9 \).

Answer:

The coordinates of the vertex are \((5,9)\)