quadratic formula practice

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What are the values of 'a', 'b', and 'c' in the quadratic equation x² + 4x + 3 = 0?

Back

In the equation x² + 4x + 3 = 0, a = 1, b = 4, and c = 3.

Front

How do you identify the 'a' value in a quadratic equation?

Back

The 'a' value is the coefficient of the x² term in the quadratic equation of the form ax² + bx + c.

Front

What does the discriminant (b² - 4ac) tell us about the roots of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

How can you solve the equation 2x² - 9x - 35 = 0 using the Quadratic Formula?

Back

Identify a = 2, b = -9, c = -35, then apply the Quadratic Formula to find x = -5/2 and x = 7.

Front

What is the first step in using the Quadratic Formula to solve a quadratic equation?

Back

The first step is to rearrange the equation into the standard form ax² + bx + c = 0.

Front

What is the significance of the ± symbol in the Quadratic Formula?

Back

The ± symbol indicates that there are two possible solutions for x, one for addition and one for subtraction.

Front

How do you convert the equation 9x² = 4 + 7x into standard form?

Back

Rearrange it to 9x² - 7x - 4 = 0.

Front

What are the solutions to the equation 2x² - x - 3 = 0 using the Quadratic Formula?

Back

The solutions are x = 3/2 and x = -1.

Front

What is the process to find the roots of a quadratic equation using the Quadratic Formula?

Back

1. Identify a, b, and c. 2. Calculate the discriminant. 3. Substitute into the formula. 4. Simplify to find the roots.