Question

a. Identify the form the quadratic is written in andstate the feature of the parabola that could befound.i. y = (x + 2)² - 5Answer:ii. y =- x² + 7x-12Answer:y = (x –9)(x +4)Answer:

Answer 1

i)

The vertex form of a quadratic equation of a parabola opening upwards or downwards is,

$y=a(x-h)^2+k\ldots\ldots(1)$

Here, (h,k) is the coordinates of the vertex of the parabola. If a is positive, the parabola is facing up and if a is negative, the parabola is facing down.

The given equation of parabola is,

$y=(x+2)^2-5\ldots\ldots(2)$

So, the given equation is in the vertex form of the quadratic equation.

Comparing equations (1) and (2), we get

a=1, h=-2, k=-5.

Since a is positive, the parabola opens upwards. The coordinates of the vertex of the parabola is (-2,-5).