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A quadratic equation takes the form ax2 +bx+c = 0 where a, b and c are numbers. The number a cannot be zero. In this unit we will look at how to solve quadratic equations using four methods: •solution by factorisation •solution by completing the square •solution using a formula •solution using graphs
Quadratic Functions and Parabolas 1 1.1 Quadratic functions In a quadratic function, the highest power of x is 2. Examples (a) y x2 2x 3 is a quadratic function of x. (b) f(t) 2t t 10 is quadratic in t. The general form of a quadratic function of x is ax2 bx c, for some numbers a, b and c.
A quadratic function is a function that can be written in the form f(x) = a(x − h)2 + k, where a ≠ 0. The U-shaped graph of a quadratic function is called a parabola .
To solve a quadratic equation by graphing, first write the equation in standard form, ax2 1 bx 1 c 5 0. Then graph the related function. y 5 ax2 1 bx 1 c. The x-intercepts of the graph are the solutions, or roots, of ax2 1 bx 1 c 5 0.
An algebraic expression can change signs only at the x-values that make the expression zero or undefined. The zeros and undefined values make up the critical numbers of the expression, and they are used to determine the test intervals in solving quadratic and rational inequalities.
Write the quadratic equation in standard form, ax 2 + bx + c = 0. Identify the values of a, b, and c. Step 2. Write the Quadratic Formula. Then substitute in the values of a, b, and c. Step 3. Simplify. Step 4. Check the solutions.
Solve quadratic equations by using the quadratic formula. Graph parabolas using the vertex, x -intercepts, and y -intercept. Solve quadratic application problems.
