Question
Asked Nov 20, 2019
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For the function y=2x2-4x-6, determine the coordinates of the x- intercept and the y- intercept.

b) determine the equation of the axis of symmetry

c) determine the coordinate of the vertex

e) graph the function and label and indicate an appropriate scale on the axes

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Expert Answer

Step 1

First of all, to find the x-intercept put y = 0 in equation (1) and find x.

Similarly, to find the parabola’s y-intercept put x = 0 in equation (1) and simplify to get y.

Therefore, x-intercept is (-1, 0) and (3, 0) and y-intercept is (0, -6).

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y 2r246 -(1) 0 2x2-4x-6 (Put y 0) 2(x2-2x-3)0 x22x-30 x2-3x+x3=0 (x-3)(x+1)0 x 3 and 1 y 2(0)-4(0)-6 (Putx 0) y =6

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Step 2

(b) Now, the symmetry axis is defined as the vertical line or horizontal line which passes through the parabola’s vertex.

Therefore, the symmetry axis is at x = 1.

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y 2x2-4x6 -1) a 2, b-4 and c -6 b x coordinate of vertex 2a (-4) 2(2) x = 1

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Step 3

(c) The vertex’s x-coordinate is at x = 1. So put the value o...

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y 2x24x6 ...1) y 21)4(1)6 =8 vertex (1-8)

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