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vkrizh
31.12.2019 •
Mathematics
Brainliesttt asap! me : )
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.
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Ответ:
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.
Ответ:
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
Ответ:
This is how I came up with the answer \/