Question

Which of the following is the equation of the axis of symmetry of the quadratic equation y = 2(x + 7)^2 – 4?

x = 7

x = –4

x = 4

x = –7

Answer 1

y = 2(x + 7)² - 4

1.) The equation is in vertex form, y = a(x - h)² + k, where (h, k) is the vertex, so

Vertex (- 7, - 4)

Axis of Symmetry: x = - 7
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2.) x-int.: y = 0:

2(x + 7)² - 4 = 0
2(x + 7)² = 4
(x + 7)² = 4 / 2
(x + 7)² = 2
x + 7 = ± √2
x = - 7 ± √2

x-int. (- 7 ± √2, 0)
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y-int.: x = 0:

y = 2(0 + 7)² - 4
y = 2(7)² - 4
y = 2(49) - 4
y = 98 - 4
y = 94

y-int. (0, 94)
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3.) Domain: all real x; Range y > - 4
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Answer 2

thanks soooo much

Answer 3

Welcome

Answer 4

let us draw it


this is our x^2

this is our (x+7)^2 we have simply shifted the above graph 7 units left


this is our 2*(x+7)^2


so this is our final graph in which we pulled the graph 4 units low
we clearly see the parabola is symmetrical about x=-7