[PDF] [PDF] Quadratic Formula - George Brown College

[PDF] Solving Quadratics by the Quadratic Formula

x2 – 7x – 18 = 0 → This problem can be solved using the quadratic formula, but it would be faster to solve the problem by factoring Generally, factoring should be considered if the leading coefficient is a 1, meaning the problem is in the form x2 + bx + c = 0

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In general, when solving quadratic equations we are looking for two solutions Example Suppose we wish to solve x2 − 5x +6=0 We factorise the quadratic by  

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Step 5 Use the square root property to complete the solution Page 12 1 4 - 12 Example 3 USING THE METHOD OF

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Example 7: Solve using the quadratic formula, express your answer as an exact value 2 − 3 = 14 2 

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Quadratic Equations in Engineering Example: (PHY 24 00 - Physics, ME 2210 - Dynamics) A projectile is fired Method 2: Quadratic Formula: for ax² +bx+c=0, 

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A quadratic equation is an equation of the second degree, which means it These are examples of quadratic equations in the standard form (ax² + bx + c 

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Quadratic equations have just one unknown, but contain a square term as well as linear terms For example, 3 2 2 =+ x x is a quadratic equation in x 1

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Tile quadratic fmmula can be used to find the roots of a quadratic equation of the Example: Step 2: Plug in the values for a, b and c into the quadratic formula

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and x = 4 Example 13 Solve the equation 4x2 + 12x +9=0 Solution Factorising we find 4x2 

[PDF] Solving Quadratic Equations Using the Quadratic Formula

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The quadratic formula is:

When working on solving quadratic equations, it is advisable to use the quadratic formula onlywhen factoring fails.

Positive Discriminant

There are 2 real roots, and 2 x-intercepts.

Zero Discriminant

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There are 2 equal real roots, and 1 x-intercept.

Negative Discriminant

There are no real roots, and no x-intercepts.

Example 1:

Step 1:

Determine the values of a, b and c.

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Example:

Step 2:

Plug in the values for a, b and c into the quadratic formula.

Example:

Step 3:

Simplify and solve.

Example:

Example 2:

Step 1:

Determine the values of a, b, and c.

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Example:

Step 2:

Step 3:

Simplify and solve.

Example:

Since we cannot take the square root of a negative number, the equation cannot be solved further using the set of real numbers. (Note: imaginary numbers are not discussed in this hand-out).

Step 4:

State the final answer.

Example:

Since there are no real solutions for this equation, there are no x-intercepts.

Example 3:

Step 1:

Determine the values of a, b and c.

Example:

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Step 2:

Plug in the values for a, b and c into the quadratic formula.

Example:

Step 3:

Simplify and solve.

Example:

x = 4.5

Step 4:

Practice Questions:

1) Solve using the quadratic formula. Round to 2 decimal places, if necessary.

2) Find the x-intercept(s) of each quadratic relation (if any) using the quadratic

formula. ©Tutoring and Learning Centre, George Brown College, 2020 | www.georgebrown.ca/tlc

Answers:

= -0.58 = 2.58

1c) X = -0.67

1d) no real solutions

1e) X1 = 0.06 X2 = 2.'94

2a) {-3.5, 0)

2c) (-0.81, 0) and (0.53, 0)

The quadratic formula can be

derirved by completing the square and isolati11g1 x in the standard form of a quadratic rellation, y = ax 2 + bx + c,. when y =

2b) no x-intercepts

Where does the quadratic formula come from?

Step 1:

Step 2:

Step 3:

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Step 4:

Step 5:

Step 6:

Step 7:

Take the square root of both sides of the equation.

Step 8:

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Step 9:

Since both terms on the right side of the equation have a common denominator, add and subtract the two terms. ©Tutoring and Learning Centre, George Brown College, 2020 | www.georgebrown.ca/tlcquotesdbs_dbs17.pdfusesText_23