Quadratic Equations

Quadratic equations are essentially second-degree polynomials that consist of three different coefficients. They are typically written in the format of ax² + bx + c = 0. The methods employed for finding solutions include factorization, the quadratic formula, or the technique of completing the square. The graph of a quadratic equation takes the shape of a parabola, with the vertex and axis of symmetry being calculable.

Quadratic Formula

Solve by the quadratic formula. List the solutions, separated by commas.

3 x^{2} + 1 x - 10 = 0

x =

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Solving by Factoring

4 b^{2} + 8 b + 7 = 4

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Solve by Completing the Square

Solve the quadratic equation by completing the square.

x^{2} - 6 x - 2 = 0

First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form:

(x + ◻)^{2} =

(x - ◻)^{2} =

Solution:

x =

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Finding the Perfect Square Trinomial

y = (x + 3)^{2} + 2

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Finding the Quadratic Equation Given the Solution Set

Write a quadratic function

f

whose zeros are 7 and -2 .

f (x) =

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Finding a,b, and c in the Standard Form

Write the quadratic function in standard form.

f (x) = 7 x^{2} - x + 1

f (x) =

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Finding the Discriminant

Discriminant of a quadratic equation Compute the value of the discriminant and give the number of real solutions of the quadratic equation.

- 2 x^{2} + 3 x + 8 = 0

Discriminant: Number of real solutions:

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Finding the Quadratic Constant of Variation

Name: 5. The function

Q = 0.003 t^{2} - 0.625 t + 25

represents the amount of energy, in Joules, in a battery after t minutes of use. a) State the amount of energy held by the battery immediately before it was used. [1]

\begin{aligned} Q & = 0.003 t^{2} - 0.625 t + 25 \\ = 0.003 (0)^{2} - 0.625 (0) + 25 \\ Q & = 25 \end{aligned}

b) Calculate the number of minutes it takes for the energy to reach zero. [4]

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Finding the Zeros by Completing the Square

Find the zeros of the quadratic equation

2 x^{2} - 8 x - 10 = 0

by completing the square.

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Quadratic Equations

Quadratic Formula

Solving by Factoring

Solve by Completing the Square

Finding the Perfect Square Trinomial

Finding the Quadratic Equation Given the Solution Set

Finding a,b, and c in the Standard Form

Finding the Discriminant

Finding the Quadratic Constant of Variation

Finding the Zeros by Completing the Square

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