Question

Describe the key features of the graph of the quadratic function f(x) = x2 + 2x - 1 A. Does the parabola open up or down? B. Is the vertex a minimum or a maximum? C. Identify the axis of symmetry, vertex and the y-intercept of the parabola.

Answer 1

A.) it opens up because it is positive.  B.  The vertex is a minimum, because it opens up C/ The axis of symmetry is X=-1, the Vertex is (-1,-2).  The Y interecept is y= -1

Answer 2

Answer:

A). Parabola Open UP.

B). Vertex is minimum.

C). Axis of Symmetry, y-axis or say line y = -2

     Vertex = ( -1 , -2 )

      y-intercept is ( 0 , -1 ).

Step-by-step explanation:

Given Equation:

f(x) = x² + 2x - 1

We know that given equation is equation of parabola.

We write given equation in standard form of the parabola.

( x - h )² = 4a( y - k )

Consider,

y = x² + 2x - 1

x² + 2x = y + 1

x² + 2x +1² = y + 1 +1²

(x + 1)² = y + 2

So, The Vertex of the given parabola is ( -1 , -2 )

     This parabola is open up. So, the Vertex is minimum.

      Axis of symmetry is Line parallel to y-axis that is y = -2

Part A).

Parabola Open UP.

Part B).

Vertex is minimum.

Part C).

Axis of Symmetry, y-axis or say line y = -2

Vertex = ( -1 , -2 )

Now to find y-intercept put x = 0 in equation of parabola.

We get,

0 + 0 - 1 = y

y = -1

Thus, y-intercept is ( 0 , -1 ).