Methods for Solving Quadratics Assessment

Front

What is the factored form of the quadratic equation (x-5)(x+6)=0?

Back

The solutions are x = 5 and x = -6.

Front

How do you find the factors of the quadratic 4x^2 - 16x - 9?

Back

The factors are (2x-9)(2x+1).

Front

In the quadratic equation y = 16x^2 - 8x - 24, what is the 'b' value?

Back

The 'b' value is -8.

Front

What is the most efficient method to solve the equation 0.02x^2 - 0.5x + 3 = 0?

Back

The most efficient method is the Quadratic Formula.

Front

Identify the quadratic being solved in the formula x = \frac{5 \pm \sqrt{(-5)^2 - 4(2)(3)}}{2(2)}.

Back

The quadratic is 2x^2 - 5x + 3.

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

What does the discriminant (b^2 - 4ac) tell us about a quadratic equation?

Back

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

Front

How do you complete the square for the equation x^2 - 6x + 5 = 0?

Back

Rewrite as (x-3)^2 - 4 = 0.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x-h)^2 + k, where (h,k) is the vertex.

Front

What is the axis of symmetry for the quadratic equation y = 2x^2 - 4x + 1?

Back

The axis of symmetry is x = \frac{-b}{2a} = 1.