Y=x^2-10x+24.
X-intercepts?
Axis of symmetry?
Vertex?
Factored form?
Maximum or minimum?
To find the x-intercepts, we set y equal to zero and solve for x:
0 = x^2 - 10x + 24
0 = (x - 6)(x - 4)
So the x-intercepts are x = 6 and x = 4.
The axis of symmetry is the line that passes through the vertex and divides the parabola into two symmetrical halves. It can be found using the formula x = -b / (2a). In this case, a = 1 and b = -10, so the axis of symmetry is x = 5.
To find the vertex, we substitute x = 5 into the equation y = x^2 - 10x + 24:
y = (5)^2 - 10(5) + 24
y = 25 - 50 + 24
y = -1
So the vertex is (5, -1).
The factored form of the equation is already given as (x - 6)(x - 4).
Since the coefficient of the x^2 term is positive, the parabola opens upwards. This means that the vertex is the minimum point of the parabola. Therefore, the function has a minimum at the vertex (5, -1).