What is the difference between an intersection and a vertex?
A vertex is a maximum of a curve, before it goes up, after that it goes down. An intersection is the point where two lines or curves intersect, e.g. your curve and the x-axis or the y-axis.
When is something compressed or stretched?
The factor a indicates how a function was stretched or compressed. If a is greater than 1 or less than -1, then the function is stretched. If a is between 1 and -1, then the function is compressed. If a=1 or a=-1, then the graph of f is a normal parabola or an inverse normal parabola.
what is stretched
flattened · stretched · ↗elongated · ↗elongated · ↗elongated ● ↗oblong obsolete, lat.
What is stretching and compression?
Stretching in the y-direction means pulling the fabric up and down, stretching in the x-direction means pulling the fabric to the left and right. In order to compress the graph, the fabric is “pushed” together (without wrinkling it). This change can also be represented mathematically using the function term.
What is upsetting?
Compression is a relative change in length of a body subjected to compressive forces. Materials can be changed in their shape, length or thickness by upsetting. They retain their original volume, provided the material is not porous.
How can you read the stretch factor?
If there is no stretch factor a, a=1 and the function corresponds to the normal parabola (f(x)=x^2). If the stretch factor a is negative, the graph for the associated function is open downwards. If the stretch factor a is positive, the graph for the associated function is open upwards.
How do you calculate the stretch factor for parabolas?
Stretching, compression and opening If you multiply the function term f(x)=x2 by a constant factor a, the shape or the opening of the associated parabola changes. The graph of the function g with g(x)=ax2 is created. The factor a is also called stretch factor.
How do I find the equation of a parabola?
Now there are two ways to find the functional equation of the parabola: set up a system of linear equations using the three points S , P1 and P2 to calculate a , b and c. Substitute S and P1 (or P2 ) into the vertex form to get calculate the parameter a.
How can you calculate A in a parabola?
Equation with the function equation y = ax2 or f(x) = ax2 you get a parabola. where a must be non-zero. If a = 1, the parabola is called a normal parabola.
How do I stretch a parabola?
If you want to compress or stretch the normal parabola, you have to look at the parabola equation f(x)=ax2 f ( x ) = ax 2. The parabola opens upwards and is narrower* than the normal parabola. This is the normal parabola that opens upwards. The parabola opens upwards and is wider** than the standard parabola.
How does a parabola arise from the normal parabola?
The parabola is created by shifting the standard parabola 2 units to the right.
If you want to shift a normal parabola to the left or right in the coordinate system, you have to look at the parabola equation f(x)=(x−d)2 f ( x ) = ( x − d ) 2 . The normal parabola is shifted by d in the direction of the x-axis, specifically to the right for a positive d and to the left for d
When does the parabola get wider?
0Parabola is open at the top and wider (wider) than the normal parabola. The graph is compressed. −1Parabola is open below and further (wider).
What does the normal form of a parabola say?
Parabolas come in three forms: 1) the most common and important is the “general form” or “normal form” y=ax²+bx+c 2) the vertex form is used when the vertex is given or one needs the vertex y=a *(x-xs)²+ys [xs und ys sind hierbei die x- und y-Koordinaten des Scheitelpunkts] 3) the…
How do you get from vertex form to normal form?
For example, the quadratic function with the vertex form f(x)= -2(x + 1)2 +3 contains the binomial formula (x + 1)2. Solve the binomial formula. Then you get: f(x)= -2(x2 + 2x + 1) +3. Now remove the brackets and you have the normal form, namely: f(x)= -2×2 -4x +1.
Is a normal parabola?
The parabola of f(x) = x² is called the “normal parabola” because it is unchanged. There is no displacement or stretching/compression.
How do you recognize a normal parabola?
Properties of the normal parabola:The graph is symmetrical about the y-axis.The graph does not go under the x-axis.The graph has a low point at (0|0).The graph keeps growing left and right.The graph has a vertex at (0|0).
What is a shifted parabola?
The normal parabola is shifted up by adding a positive number to x^2. The graph of g(x)=x^2+10 is shifted up by 10 units compared to the graph of f(x)=x^2.
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