Question

find the coordinates of the vertex of the following parabola algebraically. write your answer as an point.
$y = -x^2 + 8x - 10$
the number of attempts on this specific problem before you are marked incorrect
answer attempt 1 out of 2

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 \( y=-x^{2}+8x - 10 \), we have \( a=- 1 \), \( b = 8 \) and \( c=-10 \).

Step2: Calculate x - coordinate of vertex

Substitute \( a=-1 \) and \( b = 8 \) into the formula \( x =-\frac{b}{2a} \). So \( x=-\frac{8}{2\times(-1)}=-\frac{8}{-2} = 4 \).

Step3: Calculate y - coordinate of vertex

Substitute \( x = 4 \) into the original equation \( y=-x^{2}+8x - 10 \). Then \( y=-(4)^{2}+8\times4-10=-16 + 32-10=6 \).

Answer:

The coordinates of the vertex are \((4,6)\)