Quadratic Formula

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What does the discriminant indicate in a quadratic equation?

Back

The discriminant indicates the nature of the roots of a quadratic equation. If it is greater than 0, there are two distinct real solutions; if it is equal to 0, there is one real solution; and if it is less than 0, there are no real solutions.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

How do you calculate the discriminant?

Back

The discriminant is calculated using the formula b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is 0?

Back

If the discriminant is 0, it means that the quadratic equation has exactly one real solution (a repeated root).

Tags

CCSS.HSA-REI.B.4B

Front

How can you find the roots of the equation 2x² + 2x - 12 using the quadratic formula?

Back

To find the roots, substitute a=2, b=2, and c=-12 into the quadratic formula: x = (-2 ± √(2² - 4(2)(-12))) / (2(2)). This simplifies to x = 2 and x = -3.

Tags

CCSS.HSA-REI.B.4B

Front

What are the steps to solve a quadratic equation using the quadratic formula?

Back

1. Identify coefficients a, b, and c from the equation. 2. Calculate the discriminant (b² - 4ac). 3. Substitute a, b, and the discriminant into the quadratic formula. 4. Simplify to find the values of x.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the coefficients a, b, and c in a quadratic equation?

Back

In a quadratic equation ax² + bx + c = 0, 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.

Tags

CCSS.HSF-IF.C.7A

Front

How do you determine the number of real solutions from the discriminant?

Back

By evaluating the discriminant: if it's positive, there are two real solutions; if it's zero, there is one real solution; if it's negative, there are no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you convert a quadratic equation from standard form to vertex form?

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To convert from standard form (ax² + bx + c) to vertex form (a(x - h)² + k), complete the square.