For a standard quadratic equation the parabola intersects the Y-axis at most

Options

A. 4 times
B. 3 times
C. 2 times
D. 1 time

Answer

To solve the question regarding how many times a standard quadratic equation intersects the Y-axis, we can follow these steps:

### Step 1: Understand the standard quadratic equation
The standard form of a quadratic equation is given by:
\[ ax^2 + bx + c = 0 \]
where \( a \), \( b \), and \( c \) are constants, and \( a \neq 0 \).

### Step 2: Identify the Y-axis intersection
To find the points where the parabola intersects the Y-axis, we need to evaluate the quadratic equation at \( x = 0 \).

### Step 3: Substitute \( x = 0 \)
Substituting \( x = 0 \) into the equation gives:
\[ a(0)^2 + b(0) + c = c \]
This means that the parabola intersects the Y-axis at the point \( (0, c) \).

### Step 4: Conclusion about intersections
Since the substitution yields a single value \( c \), it indicates that the parabola intersects the Y-axis at exactly one point.

### Final Answer
Thus, for a standard quadratic equation, the parabola intersects the Y-axis at most **1 time**.

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