Quadratic equation
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A quadratic function is a polynomial function of the form f(x) = ax^2 + bx + c, where a ≠ 0. It is a function with a degree of two, meaning the highest exponent is 2. A quadratic equation is a trinomial expression with three terms - ax^2, bx, and c. The quadratic formula, x = (-b ± √(b^2 - 4ac))/2a, is used to find the roots or solutions of a quadratic equation. The discriminant, b^2 - 4ac, determines whether the roots are real and unequal, real and equal, or imaginary and unequal.
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The document discusses first degree (linear) functions. It states that most real-world mathematical functions can be composed of formulas from three families: algebraic, trigonometric, and exponential-logarithmic. It focuses on linear functions of the form f(x)=mx+b, where m is the slope and b is the y-intercept. Examples are given of equations and how to determine the slope and y-intercept to write the equation in slope-intercept form as a linear function.
Class 10 Cbse Maths Sample Paper Term 1 Model 3
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Tangents and the discriminant
The document discusses determining tangency between curves and lines using the discriminant. It shows:
1) How to prove a line is tangent to a curve by setting their equations equal and requiring the discriminant of the resulting quadratic equation to be 0.
2) Examples that find the condition for tangency (the value of t) and the point of contact between a line y=mx+t and parabolas.
3) The process involves setting the equations equal, factorizing the quadratic, and setting the discriminant equal to 0 to determine t and the point where the factors are 0.
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Quadratic equation
- 2. Definition of Quadratic Function: •A quadratic function is a function of the form f(x) = ax2+bx+c where a, b, c are real numbers and a 0. • The expression ax2+bx+c is called a quadratic expression. • The constants a, b, and c are called the quadratic coefficient, the linear coefficient and the constant term respectively.
- 3. A quadratic function is any equation with a degree* of two. A quadratic equation is a trinomial** expression because in standard form it adds three terms (ax², bx, and c). *Degree: The highest power of any term of a polynomial . **Trinomial: The sum of terms with three terms.
- 4. QUADRATIC FORMULA •The quadratic formula is often written as:- 2 4 2 b b ac x a • The number b2-4ac is called the discriminant.
- 5. Nature of the roots There are three possibilities: I. If b2-4ac>0, then, roots are real and unequal II. If b2-4ac=0, then, roots are real and equal III.If b2-4ac<0, then, roots are imaginary and unequal