12.3 Quadratic graphs and their features — Practise

1. For $y=x^2-4$, work out $y$ when $x=-2,-1,0,1,2$.

Answer: $0,-3,-4,-3,0$ respectively.

2. State the roots of $y=x^2-9$.

Answer: $x=-3$ and $x=3$.

3. Find the $y$-intercept of $y=x^2+3x-4$.

Answer: $(0,-4)$.

4. Find the turning point of $y=(x-2)^2+1$.

Answer: $(2,1)$, a minimum.

5. Does $y=-2x^2+1$ open upwards or downwards?

Answer: Downwards because the coefficient of $x^2$ is negative.

6. For $y=(x+1)^2-4$, state the turning point and roots.

Answer: Turning point $(-1,-4)$; roots are $x=-3$ and $x=1$.

7. How many roots does $y=x^2+2$ have?

Answer: No real roots, because $x^2+2$ is always positive.

8. For $h=-t^2+4t+5$, work out $h$ at $t=0$ and $t=2$.

Answer: $5$ m and $9$ m.