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Quadratic Equations. This unit is about the solution of quadratic equations. These take the form ax2 +bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs.
Stan Ulam that graph of any quadratic function can be obtained from the core parabola, f~x! 5 x2, by applying basic transformations. We apply terminology from the core parabola to parabolas in general. The point (0, 0) is called thevertex of the core parabola, and they-axis is the axis of symmetry. The axis of symmetry is a help
General Equation of a Parabola. Preliminaries and Objectives. Preliminaries Graph of y = x2 Transformation of Graphs. Shifting graphs Stretching graphs Flipping graphs. Objectives Find the equation of a parabola, given the graph. Standard Parabola. y = x2. ( 2; 4) (2; 4) ( 1; 1) (1; 1) x. Axis of symmetry = y-axis.
1.2 Examples of quadratic functions and parabolas. pment and in visual design. Example The mirrors in torches and car headlights are shaped like parabolas; microwave receivers on the roofs of buildings and satellite TV receivers.
Quadratic Functions and Parabolas. Quadratic Functions: functions defined by quadratic expressions ( 2 + + ) the degree of a quadratic function is ALWAYS 2 - the most common way to write a quadratic function (and the way we have seen quadratics in the past) is polynomial form. ( ) = 2 + +. the graph of a quadratic function is a parabola (∪ or ∩)
equation has linear terms -2hx and -2ky-they disappear when the center is (0,O). EXAMPLE 1 Find the circle that has a diameter from (1,7) to (5, 7). Solution The center is halfway at (3,7).
General Equation of a Parabola. Preliminaries Graph of y = x2 Transformation of Graphs. Shifting graphs Stretching graphs Flipping graphs. Objectives Find the equation of a parabola, given the graph. y = x2. y. ( 2; 4) (2; 4) ( 1; 1) (1; 1) x.
