Question

algebra ii 5.2 vertex form worksheet
name davide aguilar
tell whether the quadratic function is in standard form or vertex form.

1. $y = x^{2}-2x - 35$
2. $y = 3(x - 1)^{2}+3$
3. $y=-\frac{2}{3}(x - 4)^{2}+7$
4. $y=-2x^{2}+16x - 24$

Explanation:

Step1: Recall standard and vertex forms

The standard form of a quadratic function is $y = ax^{2}+bx + c$ and the vertex - form is $y=a(x - h)^{2}+k$.

Step2: Analyze $y=x^{2}-2x - 35$

It is in the form $y = ax^{2}+bx + c$ (where $a = 1$, $b=-2$, $c=-35$), so it is in standard form.

Step3: Analyze $y = 3(x - 1)^{2}+3$

It is in the form $y=a(x - h)^{2}+k$ (where $a = 3$, $h = 1$, $k = 3$), so it is in vertex form.

Step4: Analyze $y=-\frac{2}{3}(x - 4)^{2}+7$

It is in the form $y=a(x - h)^{2}+k$ (where $a=-\frac{2}{3}$, $h = 4$, $k = 7$), so it is in vertex form.

Step5: Analyze $y=-2x^{2}+16x - 24$

It is in the form $y = ax^{2}+bx + c$ (where $a=-2$, $b = 16$, $c=-24$), so it is in standard form.

Answer:

1. Standard form
2. Vertex form
3. Vertex form
4. Standard form