To find the vertex of the graph of the equation y = 4x + 22 – 5, we first need to rewrite the equation correctly. This equation can appear a bit confusing at first. Let’s consider what we have:
Firstly, the equation simplifies to:
y = 4x + 17
In this case, we can see that this is a linear equation, not a quadratic one. Generally, the vertex is determined in the context of a quadratic function, which has the form y = ax2 + bx + c.
However, if we were to discuss it hypothetically as a quadratic function, we might transform this linear equation into vertex form through a minor manipulation:
y = 4(x + 0) + 17
From this, we can see that the equation represents a slope of 4 with a y-intercept at 17. Since we are dealing with a linear equation, it does not have a vertex in the conventional sense since it extends infinitely in both directions and does not create a curve.
In summary, a linear equation does not possess a vertex. However, if the function were quadratic, we would look for the vertex using the formula:
- Vertex: (-b/2a, f(-b/2a))
Where a is the coefficient of x2 and b is the coefficient of x.
If your equation involves a quadratic function instead, feel free to share it, and I can help you determine the vertex accurately.