Step 1: Expand the Vertex Form. First, we expand the vertex form: y=3(x−2)2+5. Step 2: Convert to Standard Form. The equation is already in standard form after expansion. Step 3: Factor the Quadratic Expression. To factor the quadratic expression, we look for two numbers that multiply to ac=317 and add up to ab=−4.
If given two points, first find the slope (m) of the line that contains the points. Then write an equation in slope-intercept form (y=mx+b) and substitute in the x and y values for one of the points to find the y-intercept (b). Then convert to standard form (Ax+By=C) by subtracting the (mx) term from each side.
Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola. The vertex of a parabola is the point at the top or bottom of the parabola. 'h' is -6, the first coordinate in the vertex. 'k' is -4, the second coordinate in the vertex. 'x' is -2, the first coordinate in the other point.
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You can find the standard form of the parabola when given the vertex form of the parabola. To determine the standard form from vertex form, you will begin by expanding or squaring the ( x − h ) quantity. You will then distribute the value of a (if there is an a value). Finally, you will combine like terms.
Finding the vertex of the quadratic by using the equation x=-b/2a, and then substituting that answer for y in the orginal equation. Then, substitute the vertex into the vertex form equation, y=a(x-h)^2+k. (a will stay the same, h is x, and k is y).
There are numerous specific torts including trespass, assault, battery, negligence, products liability, and intentional infliction of emotional distress. There are also separate areas of tort law including nuisance, defamation, invasion of privacy, and a category of economic torts.
The plaintiff will be barred from recovering damages if the jury finds that the contributory fault of the plaintiff is more than 50 percent of the proximate cause of the injury. Otherwise, any economic or non-economic damages allowed will be reduced in proportion to the amount of fault attributable to the plaintiff.