Quadratic Formula and Graphs of Quadratic Equations

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What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

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What does the vertex of a parabola represent?

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The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

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What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

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How do you determine the number of solutions for a quadratic equation?

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The number of solutions can be determined by the discriminant (D = b² - 4ac). If D > 0, there are two solutions; D = 0 means one solution; D < 0 indicates no real solutions.

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What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the graph of the parabola crosses the x-axis, found by setting y = 0 in the equation.

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What is the significance of the coefficient 'a' in a quadratic equation?

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The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

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

Back

To convert from standard form (y = ax² + bx + c) to vertex form (y = a(x-h)² + k), complete the square.

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What is the factored form of a quadratic equation?

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The factored form is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots or x-intercepts of the equation.

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What is the y-intercept of a parabola?

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The y-intercept is the point where the graph crosses the y-axis, found by evaluating the equation at x = 0.