4. What key features of a quadratic graph can be identified and how are the graphs affected when the constants or coefficients are added to the parent quadratic equations? Compare the translations to the graph of linear function. Create examples of your own to explain the differences and similarities.

Standard quadratic equation ... y = a x^2 + b x + c

parabola 'a' not equal to zero

a<0 parabola opens downward

a>0 parabola opens upward

when |a| >>0 the parabola is narrower

when |a| is close to zero, the parabola is flatter

when the constant is varied it only effects the vertical position of the parabola, the shape remains the same