q(x)=−x2+6x−5q(x)=−x2+6x−5

Step 1 of 4 :

Find the vertex.

To find the vertex of the quadratic function \( q(x) = -x^2 + 6x - 5 \), we can use the vertex formula. For a quadratic function in the form \( ax^2 + bx + c \), the x-coordinate of the vertex is given by:

\[
x = -\frac{b}{2a}
\]

Here, \( a = -1 \) and \( b = 6 \).

1. **Find the x-coordinate of the vertex:**

\[
x = -\frac{6}{2(-1)} = \frac{6}{2} = 3
\]

2. **Find the y-coordinate of the vertex by substituting \( x = 3 \) back into the function:**

\[
q(3) = - (3)^2 + 6(3) - 5
\]

\[
q(3) = -9 + 18 - 5 = 4
\]

3. **So, the vertex is \( (3, 4) \).**

This is the highest point on the graph since the parabola opens downward (because \( a = -1 \)).

Would you like more details or have any questions about this step? Here are some related questions you might find useful:

1. How do you determine the direction in which a parabola opens?
2. What is the significance of the vertex in a quadratic function?
3. Can you explain how to complete the square to find the vertex?
4. How do you find the axis of symmetry for a quadratic function?
5. What are some applications of finding the vertex in real-world scenarios?

**Tip:** Always check whether the coefficient \( a \) is positive or negative to determine whether the vertex represents a maximum or minimum point.

Learn how to find the vertex of the quadratic function q(x) = -x^2 + 6x - 5 step-by-step. Understand the vertex formula and its application. Suitable for high school students studying quadratic functions.

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