y=x^2-8x+15.
Does the relation have a maximum or minimum value? Identify the y-intercept. Factor the equation. Identify x-intercepts of the relation. What is the equation of the axis of symmetry. Find the coordinates of the vertex.
1. The given relation is a quadratic equation in the form of y = ax^2 + bx + c. Since the coefficient of the x^2 term is positive (a = 1), the relation has a minimum value.
2. To identify the y-intercept, plug in x = 0 into the equation:
y = 0^2 - 8(0) + 15
y = 15
Therefore, the y-intercept is at (0, 15).
3. To factor the equation, we can rewrite it as:
y = (x - 3)(x - 5)
4. To find the x-intercepts, set y = 0 and solve for x:
0 = x^2 - 8x + 15
0 = (x - 3)(x - 5)
x = 3, 5
Therefore, the x-intercepts are at (3, 0) and (5, 0).
5. The equation of the axis of symmetry can be found using the formula:
x = -b / (2a)
In this case, a = 1 and b = -8
x = -(-8) / (2*1)
x = 4
So, the equation of the axis of symmetry is x = 4.
6. To find the coordinates of the vertex, use the axis of symmetry (x = 4) to find the y-coordinate:
y = (4)^2 - 8(4) + 15
y = 16 - 32 + 15
y = -1
Therefore, the vertex is at (4, -1).