Question

1. write the equation of the parent quadratic function.
2. what is the vertex of the parent quadratic function?
3. what is the axis of symmetry of the parent quadratic function?
4. what is the y - intercept of the parent quadratic function?
5. is the vertex of the parent quadratic function a maximum or a minimum? explain in one sentence.

Explanation:

Step1: Define parent quadratic function

The simplest quadratic function is the parent function.
$y = x^2$

Step2: Find vertex of parent function

For $y=x^2$, vertex is at $(0,0)$ (minimum point).
No expression needed.

Step3: Identify axis of symmetry

Axis of symmetry is vertical line through vertex.
$x = 0$

Step4: Calculate y-intercept

Set $x=0$ in $y=x^2$.
$y = 0^2 = 0$

Step5: Classify vertex as min/max

The coefficient of $x^2$ is positive, so parabola opens upward, making the vertex a minimum.
No expression needed.

Answer:

1. $y = x^2$
2. $(0, 0)$
3. $x = 0$
4. $0$ (the point $(0,0)$)
5. The vertex is a minimum because the coefficient of $x^2$ in $y=x^2$ is positive, so the parabola opens upward, and the vertex is the lowest point on the graph.