Quadratics (Edexcel A-Level Mathematics): Quizzes

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Discriminants
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What is the formula for the discriminant Δ\Delta of ax2+bx+c=0ax^2 + bx + c = 0?

Δ=b24ac\Delta = b^2 - 4ac

What does Δ>0\Delta > 0 indicate about the roots of a quadratic equation?

Two distinct real roots

What does Δ=0\Delta = 0 indicate about the roots of a quadratic equation?

One real root (repeated)

What type of roots occur when Δ<0\Delta < 0 for a quadratic equation?

Complex (conjugate pairs)

For 3x2+2kx+k=03x^2 + 2kx + k = 0, what is Δ\Delta?

4k212k4k^2 - 12k

For 3x2+2kx+k=03x^2 + 2kx + k = 0, what range of kk gives two distinct real roots?

k<0k < 0 or k>3k > 3

For y=ax2+bx+cy = ax^2 + bx + c, when does the parabola open upwards?

a>0a > 0

What is the x-coordinate of the vertex of y=ax2+bx+cy = ax^2 + bx + c?

x=b2ax = -\frac{b}{2a}

What is the y-intercept of y=ax2+bx+cy = ax^2 + bx + c?

cc

For y=x24x+3y = x^2 - 4x + 3, what is the value of Δ\Delta?

44

For y=x24x+3y = x^2 - 4x + 3, what are the coordinates of the vertex?

(2,1)(2, -1)

How many x-intercepts does a parabola have when Δ=0\Delta = 0?

One (vertex touches x-axis)

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