What makes a parabola stretch or compress?
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.
How can a transformed quadratic equation be used real life situations?
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product’s profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.
What is vertical stretch and compression?
What is compression in quadratic equation?
Stretch or compress by changing the value of a . You can represent a stretch or compression (narrowing, widening) of the graph of f(x)=x2 f ( x ) = x 2 by multiplying the squared variable by a constant, a . f(x)=ax2. The magnitude of a indicates the stretch of the graph.
What is a parabolic curve?
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. The point where the parabola intersects its axis of symmetry is called the “vertex” and is the point where the parabola is most sharply curved.
How are parabolas used in real life?
Parabolas are frequently used in physics and engineering for things such as the design of automobile headlight reflectors and the paths of ballistic missiles. Parabolas are frequently encountered as graphs of quadratic functions, including the very common equation y=x2 y = x 2 .
What are real life examples of quadratic equations?
Balls, Arrows, Missiles and Stones. When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster … and a Quadratic Equation tells you its position at all times!
What compression means?
The definition of compression is the action or state of being squished down or made smaller or more pressed together. When a pile of material is squished together and made smaller and more dense, this is an example of compression.
What is stretch or compression in math?
In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.
How do you stretch a parabola?
In order to vertically shrink a function, you must multiply the entire function by a number between zero and one. This compresses the function; its y-values change slower than they did prior to the transformation. In the case of a quadratic equation, the parabola appears to widen across the coordinate plane.
What is the transformation of a parabola?
The vertex of a parabola is the turning point of the parabola. It is the point on the parabola at which the curve changes from increasing to decreasing or vice-versa. The transformation can be a vertical/horizontal shift, a stretch/compression or a refrection.
How do you write a parabola equation?
The standard equation of a parabola is. y = a x 2 + b x + c . But the equation for a parabola can also be written in “vertex form”: y = a ( x − h ) 2 + k. In this equation, the vertex of the parabola is the point ( h , k ) .
What is the x – intercept of a parabola?
An x-intercept is the point where a parabola crosses the x-axis. This point is also known as a zero, root, or solution.