What is the axis of symmetry and vertex for the graph y = 2x2 + 8x - 3.
Solution:
Given, the function is f(x) = 2x2 + 8x - 3 ---------- (1)
We have to identify the vertex and the axis of symmetry of the function.
The equation of the parabola in quadratic form is given by
y = ax2 + bx + c ------------ (2)
The vertex is (h, k)
where h = -b/2a and k = (4ac - b2)/4a.
Comparing (1) and (2)
a = 2, b = 8, c = -3
So, h = -8/2(2)
= -8/4
= -2
4ac = 4(2)(-3)
4ac = -24
So, k = [-24 - (8)2]/4(2)
k = (-24 - 64)/(8)
k = -88/8
k = -11
Thus, (h, k) = (-2, -11)
The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
The axis of symmetry always passes through the vertex of the parabola.
x - coordinate of the vertex is the equation of the axis of symmetry of the parabola.
So, the axis of symmetry is x = -2
Therefore, the vertex is (-2, -11) and the axis of symmetry is x = -2.
What is the axis of symmetry and vertex for the graph y = 2x2 + 8x - 3.
Summary:
The vertex and axis of symmetry of f(x) = 2x2 + 8x - 3 are (-2, -11) and x = -2.
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