1Convert the quadratic function \( y = x^2 - 3 \) into the form \( y = a(x - h)^2 + k \) and sketch its graph.
2Convert the quadratic function \( y = x^2 - 4x + 3 \) into the form \( y = a(x - h)^2 + k \) and sketch its graph.
3Convert the quadratic function \( y = -x^2 - 2x + 3 \) into the form \( y = a(x - h)^2 + k \) and sketch its graph.
4Express \( y = x^2 + 6x + 5 \) in the form \( y = a(x - h)^2 + k \). Write its vertex, axis, intercepts and the corresponding point of its y-intercept.
5Use the formula to find the vertex of \( y = 2x^2 - 8x + 3 \). Is the vertex a maximum or a minimum point?
6Without drawing, say which way the graph of \( y = -x^2 + 2x + 1 \) opens and find its highest point.
7Why must \( a \) not be zero in the general quadratic equation \( ax^2 + bx + c = 0 \)?
8Show that the y-intercept of \( y = a(x - h)^2 + k \), with \( h = -\frac{b}{2a} \) and \( k = \frac{4ac - b^2}{4a} \), is \( c \).