How do you find the axis of symmetry and vertex point of the function: #y = -x^2 - 8x + 10#?

Question

Avery Alexander · Accepted Answer

The axis of symmetry is #x=-4#.
The vertex is #(-4,26)#.

#y=-x-8x+10# is a quadratic equation in the form #y=ax+bx+c#, where #a=-1, b=-8, c=10# Axis of Symmetry The axis of symmetry is the imaginary vertical line that divides the parabola into two equal halves. The formula for the axis of symmetry is #x=(-b)/(2a)#. #x=(-b)/(2a)=(-(-8))/(2(-1))=8/(-2)=-4# The axis of symmetry is #x=-4#. This is also the #x# value of the vertex. Vertex The vertex is the maximum or minimum point of the parabola. Since #a# is a negative number in this equation, the parabola opens downward so the vertex is the maximum point. Since we know that #x=-4#, we substitute it into the equation and solve for #y#. #y=-x^2-8x+10# #y=-(4)^2-(8)(-4)+10=# #y=-16+32+10=26# The vertex is #(-4,26)# graph{y=-x^2-8x+10 [-18.16, 13.86, 14.09, 30.11]}

Eva Adamson · Answer

undefined To find the axis of symmetry of a quadratic function in the form y = ax^2 + bx + c, you can use the formula x = -b / (2a). For the given function y = -x^2 - 8x + 10, the coefficient of x^2 is a = -1 and the coefficient of x is b = -8.

Substituting these values into the formula, you get x = -(-8) / (2*(-1)), which simplifies to x = 4. This is the x-coordinate of the vertex point.

To find the y-coordinate of the vertex point, substitute the value of x = 4 into the original function. So, y = -4^2 - 8*4 + 10, which simplifies to y = -16 - 32 + 10, giving y = -38.

Therefore, the vertex point is (4, -38), and the axis of symmetry is the vertical line x = 4.