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Explain the Vertex Formula ?
The vertex formula is a convenient way of finding the vertex of the graph for any quadratic function. The graph of the quadratic equation f(x) = ax2 + bx + c has its vertex at:
(-b/2a, f(-b/2a))
In other words the x coordinate of the vertex is always x = -b/2a, which is also the equation for the axis of symmetry.
SymmetryNote: this formula is derived from the standard form by completing the square.Here's an example that you can look at:
Question: Use the vertex formula to find the vertex of the graph of the following function:f(x) = -x 2 + 6x - 5 Solutions: Find the x-coordinate of the vertex first, using the vertex formula. x = -b /2aX = -6 / 2(-1)X = -6/-2X =3This tells us that the vertex is the point (3, ?). We now need to find the y-coordinate, or functional value, forx = 3. f(3) = -(3) 2 + 6(3) - 5= -9 + 18 -5= 4So, the vertex point of f(x) = -x2 +6x - 5 is the point (3,4)
Evaluate the given limit. Solution : It is a combination of many of the functions listed above and none of the limited are violated so all we have to do is plug in x = 3
Charlie needs to know the area of his property, that measures 120 ft through 150 ft. Which formula will he use? The area of a rectangle is length × width.
If the area of a small size pizza is 78.5 in 2 , what size pizza box would required for the small pizza? (Note: Pizza boxes are calculated according to the length of one side.)
Arc Length and Surface Area Revisited We won't be working any instances in this part. This section is here exclusively for the aim of summarizing up all the arc length and su
NUMBER SYSTEMS: Numbers are intellectual witnesses that belong only to mankind. Example: If the H C F of 657 and 963 is expressible in the form of 657x + 963 x -
How do I reverse calculate taxes?
Jay bought twenty-five $0.37 stamps. How much did he spend? To ?nd how much Jay spent, you must multiply the cost of each stamp ($0.37) through the number of stamps purchased (
reduction
Find out the x-y coordinates of the points in which the following parametric equations will have horizontal or vertical tangents. x = t 3 - 3t y = 3t 2 - 9 Solut
Bill traveled 117 miles in 2.25 hours. What was his average speed? Use the formula d = rt (distance = rate × time). Substitute 117 miles for d. Substitute 2.25 hours for t and
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