I'm stuck on graphing this quadratic equation:
%2B%204x%20%2B%203" id="TexFormula1" title="y \leqslant {x}^{2} + 4x + 3" alt="y \leqslant {x}^{2} + 4x + 3" align="absmiddle" class="latex-formula">
1 answer:
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Answer:
(3, 0 )
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c (a ≠ 0 )
Then the x- coordinate of the vertex is
= -
y = 5x² - 30x + 45 ← is in standard form
with a = 5, b = - 30 , then
= -
= 3
Substitute x = 3 into the function for corresponding value of y
y = 5(3)² - 30(3) + 45 = 45 - 90 + 45 = 0
vertex = (3, 0 )
15 inches.
The side length of the base is 4. Find the surface area of the base only by squaring the side length - 4² - which is 16. The surface area of the base is 16 in².
The surface area of the entire pyramid can be found using this equation:
Where:
- SA is the surface area (136 square inches)
- B is the area of the base (16 square inches)
- n is the number of triangles (4, because it's a square pyramid)
- b is the base length (4 inches)
- l is the slant length
Note that we have many parts of this equation, and all we need is the slant length. So, let's format the equation with what we have:
So then we want to solve for l, the slant height. So, start by subtracting 16 from each side. This would give us:
Now, multiply both sides by 2 to get rid of the fraction:
Finally, divide both sides by four, twice (divide by 16):
So, we know that the slant height of this pyramid is 15 inches.
The side length of the base is 4. Find the surface area of the base only by squaring the side length - 4² - which is 16. The surface area of the base is 16 in².
The surface area of the entire pyramid can be found using this equation:
Where:
- SA is the surface area (136 square inches)
- B is the area of the base (16 square inches)
- n is the number of triangles (4, because it's a square pyramid)
- b is the base length (4 inches)
- l is the slant length
Note that we have many parts of this equation, and all we need is the slant length. So, let's format the equation with what we have:
So then we want to solve for l, the slant height. So, start by subtracting 16 from each side. This would give us:
Now, multiply both sides by 2 to get rid of the fraction:
Finally, divide both sides by four, twice (divide by 16):
So, we know that the slant height of this pyramid is 15 inches.