express (5x - 3)(x - 2) in intercept form of quadratic equation

To express the quadratic equation in intercept form, we start with the expanded form of \((5x - 3)(x - 2)\):

\[ 5x^2 - 13x + 6 \]

The intercept form (also known as factored form) of a quadratic equation is:

\[ y = a(x - p)(x - q) \]

where \( p \) and \( q \) are the x-intercepts of the quadratic function.

In our case, we already have the factors from the original expression:

\[ (5x - 3)(x - 2) \]

To express this in intercept form, we need to ensure it matches the structure of \( a(x - p)(x - q) \). We can rewrite each factor as follows:

\[ 5x - 3 = 5(x - \frac{3}{5}) \]
\[ x - 2 = x - 2 \]

Now, we can combine them into the intercept form:

\[ y = 5(x - \frac{3}{5})(x - 2) \]

So, the intercept form of the quadratic equation \((5x - 3)(x - 2)\) is:

\[ y = 5(x - \frac{3}{5})(x - 2) \]

Would you like more details or have any questions?

Here are 5 related questions you might ask:
1. How do you find the x-intercepts of a quadratic equation?
2. What is vertex form of a quadratic equation?
3. How do you convert from standard form to intercept form?
4. Can you show an example of finding the vertex of a quadratic function?
5. How do you graph a quadratic function given its intercept form?

**Tip:** To convert a quadratic equation to intercept form, factor the quadratic expression and identify the x-intercepts from the factors.

Learn how to express the quadratic equation (5x - 3)(x - 2) in intercept form with a step-by-step solution. This problem involves factoring and identifying intercepts, essential concepts in algebra and quadratic equations. Suitable for students in Grades 9-12.

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