Question

why does the graph of (y = 2x^2 - 4x + 5) have no zeroes?

because when (x = 1, y = 3)
because it crosses the y-axis once
because (x = 0) is the only value of x that makes the equation true
because (2x^2 - 4x + 5 \
eq 0)

Explanation:

Identify the definition of zeroes

Using the Quadratic Relations knowledge point

$$ \text{Zeroes of } y = f(x) \text{ occur where } f(x) = 0. $$

Analyze the given equation

Using the Quadratic Relations knowledge point

$$ y = 2x^2 - 4x + 5 $$

Evaluate the condition for no zeroes

Using the Quadratic Relations knowledge point

$$ 2x^2 - 4x + 5 eq 0 \quad \forall x \in \mathbb{R} $$

Match with the given options

Using the Quadratic Relations knowledge point

$$ \text{Option 4: "Because } 2x^2 - 4x + 5 eq 0\text{" matches the algebraic condition.} $$

Answer:

• Because when \(x = 1, y = 3\)
• Because it crosses the y-axis once
• Because \(x = 0\) is the only value of x that makes the equation true
• **Because \(2x^2 - 4x + 5

eq 0\) (Correct answer)**