Question

Graph each function. Identify the y-intercept, axis of symmetry, and vertex of

each function. Does the vertex represent a maximum or minimum value?
1. f(x) = x² + 1
2. f(x) = -x² + 4x - 2
3. f(x) = 2x² + 4x - 6

Answer 1

The quadratic equations are identified as follows

1. f(x) = x² + 1

y-intercept = vertex (maximum) = A (0, 1)

axis of symmetry, x = 0

2. f(x) = -x² + 4x - 2

vertex (maximum) = A (2, 2)

axis of symmetry, x = 2

y-intercept = B. (0, 2)

3. f(x) = 2x² + 4x - 6

vertex (minimum) = A (-1, -8)

axis of symmetry, x = -1

y-intercept = B. (0, 6)

What is vertex and axis of symmetry of a quadratic equation

In the context of a quadratic equation, the vertex is the point where the graph reaches its minimum (if a > 0) or maximum (if a < 0) value.

where a is the coefficient of x². The vertex coordinates is represented as (h, k)

The axis of symmetry is a vertical line that passes through the vertex of the parabola. The equation of the axis of symmetry is (x = h\

where \(h\) is the x-coordinate of the vertex.

Also, the y-intercept is the point the curve intersects the y-axis

The graphs are attached.