Quadratic Formula - Pre-Test

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What is the quadratic formula?

Back

The quadratic formula is given by x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c = 0.

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How do you identify the coefficients a, b, and c in a quadratic equation?

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In a quadratic equation of the form ax^2 + bx + c = 0, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant term.

Front

What does the discriminant of a quadratic equation tell you?

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The discriminant, given by b^2 - 4ac, determines the nature of the roots of the quadratic equation. If it is positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

How do you solve a quadratic equation using the quadratic formula?

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To solve a quadratic equation using the quadratic formula, identify the coefficients a, b, and c, substitute them into the formula, and simplify to find the values of x.

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What is the significance of the vertex in a quadratic function?

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The vertex of a quadratic function represents the maximum or minimum point of the parabola, depending on the direction it opens. It can be found using the formula x = -\frac{b}{2a}.

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What is the standard form of a quadratic equation?

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The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What is the vertex form of a quadratic equation?

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

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

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To convert from standard form to vertex form, you can complete the square.

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What is the axis of symmetry in a quadratic function?

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The axis of symmetry of a quadratic function is a vertical line that passes through the vertex, given by the equation x = -\frac{b}{2a}.

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What are the roots of a quadratic equation?

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The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.