Forms of Quadratic Equations

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Questions and Answers

What does the factored form of a quadratic equation reveal about the parabola?

  • The x-intercepts (zeros) of the parabola. (correct)
  • The area under the parabola.
  • The y-intercepts of the parabola.
  • The vertex of the parabola.

What is the general form of a quadratic equation represented in standard form?

  • a(x - h)² + k = 0
  • ax² + bx + c = 0 (correct)
  • a(x + b)(x + c) = 0
  • x² - (h + k)x + hk = 0

How can you determine the x-coordinate of the vertex from the factored form?

  • By applying the quadratic formula.
  • By completing the square.
  • By averaging the x-intercepts. (correct)
  • By substituting the y-intercepts.

In which form of the quadratic equation can you directly find the coordinates of the vertex?

<p>Vertex form (C)</p> Signup and view all the answers

Which method can be used to convert a quadratic equation from standard form to vertex form?

<p>Completing the square (C)</p> Signup and view all the answers

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Flashcards

Factored Form

A way to write a quadratic equation by showing the factors that multiply to equal zero. This form quickly reveals the x-intercepts, also known as the zeros of the parabola.

Standard Form

The most common representation of a quadratic equation, written as ax² + bx + c = 0, where 'a', 'b', and 'c' are constants. This form is useful for applying the quadratic formula.

Vertex Form

This form reveals the vertex of the parabola directly with the coordinates (h, k). The equation is written as a(x - h)² + k = 0.

Vertex

The point where the parabola changes direction - either its highest or lowest point. It's represented by the coordinates (h, k) in vertex form.

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X-intercepts (also called Zeros)

The x-values where the parabola crosses the x-axis. These are also the solutions to the quadratic equation.

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Study Notes

Forms of Quadratic Equations

  • Quadratic equations create parabolas.
  • Three forms: factored, standard, and vertex.
  • Each form has advantages and disadvantages.
  • Factored form shows x-intercepts (roots).
  • Standard form is used for the quadratic formula.
  • Vertex form directly shows the parabola's vertex.
  • Vertex is (h, k), h is the opposite of the value in vertex form, k is the y-value.

Understanding the Different Forms

  • Factored form: (x + a)(x + b) = 0. X-intercepts are x = -a and x = -b.
  • Standard form: ax² + bx + c = 0. Used for the quadratic formula to find x-intercepts.
  • Vertex form: a(x - h)² + k = 0. Shows vertex coordinates (h, k) directly.

Connecting the Forms

  • Convert factored to vertex form by finding the midpoint of x-intercepts (the x-coordinate of the vertex).
  • Substitute the x-value into the original function to find the y-coordinate of the vertex.
  • Convert standard to vertex form using completing the square.

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