Conics - Parabola - General Practice Problems Online

If the two parabolas $y=2x^2-3x+6$ and $y=-2x^2-ax+1$ meet at a single point, what is the product of all possible values for $a?$

What is the range of $a$ such that the roots of $2x^2+ax+17=0$ are larger than $-17?$

{35}<a<{68}

-2\sqrt{34}\leq a\leq 2\sqrt{34}

a\leq -2\sqrt{34}

or

2\sqrt{34}\leq a<{35}

a\leq -2\sqrt{34}

or

a>{68})

Consider a parabola $y=3x^2-5x+2$ and a line that passes through $(-2,0)$ on the coordinate plane. If the parabola and line intersect at exactly two distinct points, what is the possible range for the slope $m$ of the line?

m<{-17}-2\sqrt{69}

or

m>{-17}+2\sqrt{69}

{-17}-2\sqrt{69}<m<{-17}+2\sqrt{69}

{-17}-2\sqrt{72}<m<{-17}+2\sqrt{72}

m<{-17}-2\sqrt{72}

or

m>{-17}+2\sqrt{72}

Find the vertex of the parabola $y=4x^2+5x+5.$

\left(\frac{5}{8},\frac{55}{16}\right)

\left(-\frac{5}{8},\frac{55}{16}\right)

\left(\frac{5}{8},\frac{55}{8}\right)

\left(-\frac{5}{8},\frac{55}{8}\right)

A parabola passes through the following three points: $(3,0), (9,0), (1,64).$ What is the vertex of the parabola?

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