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graph f(x) = x^2 + 2x - 3, label the function’s x-intercepts, y-intercept and vertex with their coordinates. also draw in and label the axis of symmetry. explain and show your work.

x-intercepts: (-3,0), (1,0)

work:

0 = x^2 + 2x - 3

quadratic equation: x = -2 +√(2^(2) - 4 × 1(-3)) / (2 × 1) = 1

quadratic equation: x = -2 -√(2^(2) - 4 × 1(-3)) / (2 × 1) = -3

(x,y) --) (-3,0), (1,0)

y-intercept: (0,-3)

work:

y = (0)^2 + 2(0) - 3

y = -3

(x,y) --) (0,-3)

vertex: (-1,-4)

work:

xv = -( b / (2a) )

a = 1, b = 2, c = -3

xv = -( 2 / (2×1) )

xv = -1

yv = (-1)^2 + 2(-1) - 3

yv = -4

(x,y) --) (-1,-4)

axis of symmetry: -1

work:

a = 1 in the x^(2) + 2ax + a^(2)

x^(2) + 2x + 1^(2) = (x + 1)^(2)

(x + 1)^(2) - 3 - 1^(2)

y = (x + 1)^(2) - 4

y + 4 = (x - 1)^(2)

put in standard form --) 4 × 1/4( y -( -4 ) ) = ( x -( -1) )^(2)

(h,k) = (-1,-4); p = 1/4

in parabola form expression: 4p( y - k ) = ( x - h )^(2) and is symmetric around the y-axis at -1.

Here's what I get  

Step-by-step explanation:

1. Graph the parabola

(a) Create a table containing a few values of x and y

I chose the following points:

(b) Plot your points

Draw dots at the coordinates of each point ( Fig. 1).

(c) Draw the graph

Draw a smooth line through the points.

Extend your line smoothly to the edge of the plot area (Fig. 2).

2. Label the intercepts and vertex

The x-intercepts are at (-3, 0) and (1, 0).

The y-intercept is at (0, -3).

The vertex is at (-1, -4).

See Fig.3 for the labels.

3. Axis of symmetry

The axis of symmetry is a vertical line that passes through the vertex and divides the graph into mirror- image halves.

The vertex is at (-1, -4), so the vertex is a straight line passing through (-1, -4) and (-1, 0). It is the dashed black line in Fig. 4

35-60 students are taking math.