Write the equation in standard form.identify a,b,and c y=4(x-2)^2-6

To write the equation in standard form, we'll expand and simplify the given equation \( y = 4(x - 2)^2 - 6 \).

### Step 1: Expand \( (x - 2)^2 \)

\[
(x - 2)^2 = x^2 - 4x + 4
\]

### Step 2: Multiply by 4

\[
4(x^2 - 4x + 4) = 4x^2 - 16x + 16
\]

### Step 3: Subtract 6 from the result

\[
y = 4x^2 - 16x + 16 - 6
\]

\[
y = 4x^2 - 16x + 10
\]

### Standard Form

The equation is now in standard form: 

\[
y = 4x^2 - 16x + 10
\]

### Identify \(a\), \(b\), and \(c\)

For the quadratic equation \( y = ax^2 + bx + c \):

- \( a = 4 \)
- \( b = -16 \)
- \( c = 10 \)

---

Would you like a detailed explanation of any steps or have any other questions?

Here are 5 related questions for further exploration:
1. How do you find the vertex of a quadratic equation in standard form?
2. What is the axis of symmetry for the equation \( y = 4x^2 - 16x + 10 \)?
3. How do you convert a quadratic equation from standard form to vertex form?
4. How does the value of \(a\) affect the shape of the parabola?
5. What are the roots of the equation \( y = 4x^2 - 16x + 10 \)?

**Tip**: The discriminant \(b^2 - 4ac\) helps determine the number and type of roots of a quadratic equation.

Write the equation in standard form. Identify a, b, and c: y = 4(x-2)^2 - 6

Explore how to write the quadratic equation y = 4(x-2)^2 - 6 in standard form with step-by-step instructions. Learn how to identify the coefficients a, b, and c for this quadratic equation, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation