Quadratic Formula Warmup

Answer explanation

In the equation x^2 + 8x - 3 = 0, the standard form is ax^2 + bx + c. Here, a = 1 (coefficient of x^2), b = 8 (coefficient of x), and c = -3 (constant term). Thus, the correct values are a=1, b=8, c=-3.

Answer explanation

The correct choice is the third one, which properly applies the quadratic formula. It uses -6 for the coefficient of x, includes the correct discriminant calculation with -16, and follows the formula structure.

Answer explanation

The correct forms of the quadratic formula for the equation 2x^2-7x+1=0 are: 1) \frac{-(-7) \pm \sqrt{(-7)^2-4(2)(1)}}{2(2)} and 2) \frac{(7) \pm \sqrt{(-7)^2-4(2)(1)}}{2(2)}.

• -1

• -3

• 9

• 0

• 1

• 3

• -9

Answer explanation

In the equation -x^2 - 3x + 9 = 0, the coefficients are identified as follows: a = -1 (coefficient of x^2), b = -3 (coefficient of x), and c = 9 (constant term). Thus, a = -1, b = -3, c = 9.

What does the discriminant determine?

• Whether the graph goes up or down

• The vertex

• The number of Solutions

• The y-intercept

Answer explanation

The discriminant of a quadratic equation determines the number of solutions. If it's positive, there are two solutions; if zero, one solution; and if negative, no real solutions.

What is the discriminant in the Quadratic Formula?

• -b + 4ac

• b - 4ac

• -b² - 4ac

• b² - 4ac

Answer explanation

The discriminant in the Quadratic Formula is given by b² - 4ac. It helps determine the nature of the roots of the quadratic equation. The correct choice is b² - 4ac.

What is the correct Quadratic Formula?

Answer explanation

The correct Quadratic Formula is x = \frac{-b\pm\sqrt[]{b^2-4ac}}{2a}. It is used to find the roots of a quadratic equation ax^2 + bx + c = 0, where a, b, and c are coefficients.