quadratic formula

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What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.

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What does it mean if a parabola opens upwards?

Back

A parabola opens upwards if the coefficient of x² (a) in the quadratic equation ax² + bx + c is positive.

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What does it mean if a parabola opens downwards?

Back

A parabola opens downwards if the coefficient of x² (a) in the quadratic equation ax² + bx + c is negative.

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What is the vertex of a parabola?

Back

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 the vertical line that divides the parabola into two mirror-image halves and passes through the vertex.

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What are the possible types of solutions for a quadratic equation?

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A quadratic equation can have two real solutions, one real solution (a repeated root), or no real solutions (when the discriminant is negative).

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What is the discriminant in the quadratic formula?

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The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

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How do you find the 'b' value in a quadratic equation?

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The 'b' value in a quadratic equation ax² + bx + c is the coefficient of the x term.

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What does it mean if a quadratic equation has no real solutions?

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If a quadratic equation has no real solutions, it means the graph of the equation does not intersect the x-axis, indicating that the discriminant is negative.

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How can you determine the number of solutions a quadratic equation has?

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You can determine the number of solutions by calculating the discriminant (b² - 4ac): if it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.