What is the vertex form of a quadratic equation?

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

How do you convert from standard form to vertex form?

To convert from standard form $$y = ax^2 + bx + c$$ to vertex form, complete the square.

What is the axis of symmetry in a parabola?

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

What is the role of the leading coefficient in a quadratic equation?

The leading coefficient $$a$$ determines the direction of the parabola: if $$a > 0$$ , the parabola opens upwards; if $$a

How do you factor the quadratic $$x^2 - 7x - 18$$ ?

The quadratic $$x^2 - 7x - 18$$ factors to $$(x + 2)(x - 9)$$ .

What is the factored form of $$2x^2 + 2x - 12$$ ?

The quadratic $$2x^2 + 2x - 12$$ factors to $$2(x - 2)(x + 3)$$ .

How do you find the value of n in the equation $$x^2 + nx + 72 = (x + 8)(x + 9)$$ ?

Expanding the right side gives $$x^2 + 17x + 72$$ , so $$n = 17$$ .

What is the relationship between the roots and the coefficients of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

Flashcard: Writing Quadratic Equations and Factoring Flashcards

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FLASHCARD QUESTION

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What is a quadratic equation?

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FLASHCARD QUESTION

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What does it mean to factor a quadratic equation?

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