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Pani-rosa [81]
3 years ago
11

Describe the graph of a quadratic function

Mathematics
2 answers:
maw [93]3 years ago
7 0
So, given a quadratic function, y = ax2<span> + bx + c, when "a" is positive, the </span>parabola<span> opens upward and the vertex is the </span>minimum<span> value. On the other hand, if "a" is negative, the graph opens </span>downward<span> and the vertex is the </span>maximum<span> value. To put it in complicated terms. Or when A is positive the graph is shaped like a U but if A is negative the graph is an upside down U


</span>
Nat2105 [25]3 years ago
4 0
Graphs: Hope this helps

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape. 


´

Graphs of quadratic functions have a unique symmetrical nature<span> with a maximum or minimum function value corresponding to the vertex.
</span>

´When the leading coefficient of the quadratic expression representing the function is negative the graph opens down and when positive it opens up.

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Two equalivlant expressions to 24m-12p+72
GalinKa [24]

Answer:

Step-by-step explanation:

24m - 12p + 72

factor out a 2

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3 years ago
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In the standard x,y plane, a circle has a radius 6 and center (7, 3). The circle intersects the x-axis at (a, 0) and (b, 0). Wha
arsen [322]

Answer:  The required value of a+b is 14.

Step-by-step explanation:  Given that in the standard xy plane, a circle has a radius 6 and center (7, 3).

The circle intersects the x-axis at (a, 0) and (b, 0).

We are to find the value of a+b.

We know that

the standard equation of a circle with center at (h, k) and radius r units is given by

(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

For the given circle, we have

(h, k) = (7, 3)  and  r = 6 units.

So, from equation (i), we get

(x-7)^2+(y-3)^2=6^2\\\\\Rightarrow (x-7)^2+(y-3)^2=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

Since the circle (ii) passes through the points (a, 0) and (b, 0), so let the point be denoted by (c, 0), then we have

(c-7)^2+(0-3)^2=36\\\\\Rightarrow (c-7)^2+9=36\\\\\Rightarrow (c-7)^2=27\\\\\Rightarrow c-7=\pm3\sqrt3~~~~~~~~~~~~~~~~~~~~~~[\textup{Taking square root on both sides}]\\\\\Rightarrow c=7\pm3\sqrt3

Therefore, we get

a=7+3\sqrt3,\\\\b=7-3\sqrt3.

That is,

a+b=(7+3\sqrt3)+(7-3\sqrt3)=14.

Thus, the required value of a+b is 14.

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Decimal Form: 2.25

Mixed Number Form: 2 1/4

Hope this helps! :)




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