A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola y = 2x² + 10x + 8 is (-2.5, -4.5).
What is a quadratic equation?
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower the parabola is, and the "-" or "+" that the parabola will open up or down.
The general form of a parabola is written in the form ax²+bx+c, which is a quadratic equation. While the vertex form of the parabola is written as y=a(x-h)² + k.
Given that the equation of the parabola is y = 2x² + 10x + 8. Now if we compare the general equation of the parabola with ax²+bx+c, the value of a, b, and c will be 2, 10, and 8, respectively.
Further, the vertex of the parabola can be written as,
h =−b/2a
h = -10 / 2(2)
h = -10/4
h = -2.5
k = -(b² - 4ac) / 4a
k = -[10² - 4(2)(8)] / 4(2)
k = (100 - 64) / 8
k = -36/8
k = -4.5
Hence, the vertex of the parabola y = 2x² + 10x + 8 is (-2.5, -4.5).
Learn more about Quadratic Equations:
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