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FOA/Algebra 1Unit 5: Comparing Linear, Quadratic, and Exponential FunctionsNotesUnit 5: Comparing Linear, Quadratic, & Exponential Functions After completion of this unit, you will be able to Learning.
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Representations FAQ
Linear graphs always look like a straight line with no curve. Quadratic graphs have a parabola shape. An exponential graph has a curve, but the curve will start out vertical and become more horizontal, or the curve will start out horizontal and grow to be more vertical.
Examples of quadratic equations x 2 + x − 30 = 0. 5 t 2 + 4 t + 1 = 0. 16 x 2 − 4 = 0. 3 x 2 + x = 0. 5 x 2 = 25.
Examples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc. From these examples, you can note that, some quadratic equations lack the term “c” and “bx.”
There are three commonly-used forms of quadratics: Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c. Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2) Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.
Solve a quadratic equation using the quadratic formula. Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, and c. Write the Quadratic Formula. Then substitute in the values of a, b, and c. Simplify. Check the solutions.
In other words, if you have a times the square of the expression following b plus b times that same expression not squared plus c equal to 0, you have an equation that is quadratic in form.
The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. So what I want to talk about now is an overview of all the different ways of solving a quadratic equation.
A quadratic function results in a U-shaped graph, called a parabola. The values of the function change smoothly, so the curve must be smooth as well.
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