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Viktor [21]
3 years ago
9

How to graph a quadratic equation?

Mathematics
1 answer:
Gekata [30.6K]3 years ago
6 0
Graphing Quadratic Equations Quadratic Equation A Quadratic Equation in Standard Form (a, b, and c can have any value, except that a can't be 0.) Here is an example: Quadratic Equation Graphing You can graph a Quadratic Equation using the Function Grapher, but to really understand what is going on, you can make the graph yourself. Read On! The Simplest Quadratic The simplest Quadratic Equation is: f(x) = x2 And its graph is simple too: Square function This is the curve f(x) = x2 It is a parabola. Now let us see what happens when we introduce the "a" value: f(x) = ax2 ax^2 Larger values of a squash the curve inwards Smaller values of a expand it outwards And negative values of a flip it upside down Quadratic Graph Play With It Now is a good time to play with the "Quadratic Equation Explorer" so you can see what different values of a, b and c do. The "General" Quadratic Before graphing we rearrange the equation, from this: f(x) = ax2 + bx + c To this: f(x) = a(x-h)2 + k Where: h = -b/2a k = f( h ) In other words, calculate h (=-b/2a), then find k by calculating the whole equation for x=h First of all ... Why? Well, the wonderful thing about this new form is that h and k show us the very lowest (or very highest) point, called the vertex: And also the curve is symmetrical (mirror image) about the axis that passes through x=h, making it easy to graph quadratic vertex So ... h shows us how far left (or right) the curve has been shifted from x=0 k shows us how far up (or down) the curve has been shifted from y=0 Lets see an example of how to do this: Example: Plot f(x) = 2x2 - 12x + 16 First, let's note down: a = 2, b = -12, and c = 16 Now, what do we know? a is positive, so it is an "upwards" graph ("U" shaped) a is 2, so it is a little "squashed" compared to the x2 graph Next, let's calculate h: h = -b/2a = -(-12)/(2x2) = 3 And next we can calculate k (using h=3): k = f(3) = 2(3)2 - 12·3 + 16 = 18-36+16 = -2 So now we can plot the graph (with real understanding!): 2x^2-12x+16 We also know: the vertex is (3,-2), and the axis is x=3 From A Graph to The Equation What if we have a graph, and want to find an equation? Example: you have just plotted some interesting data, and it looks Quadratic: quadratic data Just knowing those two points we can come up with an equation. Firstly, we know h and k (at the vertex): (h, k) = (1,1) So let's put that into this form of the equation: f(x) = a(x-h)2 + k f(x) = a(x-1)2 + 1 Then we calculate "a": We know (0, 1.5) so: f(0) = 1.5 And we know the function (except for a): f(0) = a(0-1)2 + 1 = 1.5 Simplify: f(0) = a + 1 = 1.5 a = 0.5 And so here is the resulting Quadratic Equation: f(x) = 0.5(x-1)2 + 1 Note: This may not be the correct equation for the data, but it’s a good model and the best we can come up with.
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One angle measure in an acute triangle is 38°. What could the measure of one of the other angles be?
Oksi-84 [34.3K]
If is an acute triangle, all the angles should be acute angles.
180-38=142°
142-69=73°
So your answer is 69°, lovely~
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4 years ago
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4 years ago
Based on the diagram what is the length of AC?
sweet [91]

Answer: 12.4

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3 years ago
My cupcake recipe makes 12 cupcakes and requires 1\12 (fraction) sticks of butter. I can only buy whole sticks of butter. How ma
o-na [289]

Answer:

Step-by-step explanation:

Answer: There are 8 cupcakes is needed to make 100 cupcakes.

Step-by-step explanation:

Since we have given that

Number of cupcakes = 12

Part of sticks of butter is needed to 12 cupcakes is given by

According to question, I can only buy whole sticks of butter.

So, to make 100 cupcakes,

Number of whole sticks of butter is given by

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6 0
3 years ago
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600kg is divided between misal and pratick so that misal gets 3/5 of the amount. How much does prayick get?
mr Goodwill [35]

Answer:

240

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2 years ago
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