For the quadratic equation x^2 + 2x + 1 = 0, what is the vertex of the parabola?
Practice Questions
Q1
For the quadratic equation x^2 + 2x + 1 = 0, what is the vertex of the parabola?
(-1, 0)
(-1, 1)
(0, 1)
(1, 1)
Questions & Step-by-Step Solutions
For the quadratic equation x^2 + 2x + 1 = 0, what is the vertex of the parabola?
Correct Answer: (-1, 0)
Step 1: Identify the coefficients a, b, and c from the quadratic equation x^2 + 2x + 1 = 0. Here, a = 1, b = 2, and c = 1.
Step 2: Use the formula for the x-coordinate of the vertex, which is -b/(2a). Plug in the values of b and a: -2/(2*1) = -2/2 = -1.
Step 3: Now, find the y-coordinate of the vertex by substituting x = -1 back into the original equation. Calculate f(-1): (-1)^2 + 2*(-1) + 1 = 1 - 2 + 1 = 0.
Step 4: Combine the x and y coordinates to find the vertex. The vertex is (-1, 0).
Quadratic Functions – Understanding the standard form of a quadratic equation and how to find the vertex using the formula.
Vertex Formula – Applying the vertex formula (-b/2a, f(-b/2a)) to determine the vertex of a parabola.
