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10.04 Optimisation

Interactive practice questions

Consider the parabola with equation $y=x^2-4x+6$y=x24x+6.

a

The vertex of a parabola is located where the derivative is $0$0. If we set the derivative of the given parabola to $0$0, we get $2x-4=0$2x4=0.

Solve this equation to find the $x$x-coordinate of the vertex.

b

Find the $x$x-coordinate of the vertex using the formula $x=-\frac{b}{2a}$x=b2a.

c

Find the $y$y-coordinate of the vertex.

d

Which of the following statements is true?

The gradient of the tangent to the parabola is positive at $\left(2,2\right)$(2,2).

A

There is a turning point at $\left(2,2\right)$(2,2).

B

The gradient of the tangent to the parabola is negative at $\left(2,2\right)$(2,2).

C
Easy
4min

The height at time $t$t of a ball thrown upwards is given by the equation $h=59+42t-7t^2$h=59+42t7t2.

Easy
3min

When an object is thrown into the air, its height above the ground is given by the equation $h=193+24s-s^2$h=193+24ss2, where $s$s is its horizontal distance from where it was thrown.

Easy
4min

A function $f:\left[-7,5\right]\to\mathbb{R}$f:[7,5] is given by $f\left(x\right)=-6x^2-12x+90$f(x)=6x212x+90.

Medium
4min
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Outcomes

2.3.21

solve optimisation problems arising in a variety of contexts involving simple polynomials on finite interval domains

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