In the expression 4x^2 - 12x + 9, what is the vertex of the parabola?

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Question: In the expression 4x^2 - 12x + 9, what is the vertex of the parabola?

Options:

Correct Answer: (1.5, -1.5)

Solution:

The vertex can be found using the formula x = -b/(2a), which gives x = 1.5. Substituting back gives the y-coordinate.

In the expression 4x^2 - 12x + 9, what is the vertex of the parabola?

In the expression 4x^2 - 12x + 9, what is the vertex of the parabola?

Step 1: Identify the coefficients a, b, and c from the expression 4x^2 - 12x + 9. Here, a = 4, b = -12, and c = 9.
Step 2: Use the formula x = -b/(2a) to find the x-coordinate of the vertex. Substitute b and a into the formula: x = -(-12)/(2*4).
Step 3: Calculate the value: x = 12/8 = 1.5.
Step 4: Now, substitute x = 1.5 back into the original expression to find the y-coordinate. Calculate y = 4(1.5)^2 - 12(1.5) + 9.
Step 5: Calculate y: y = 4(2.25) - 18 + 9 = 9 - 18 + 9 = 0.
Step 6: The vertex of the parabola is (1.5, 0).

Quadratic Functions – Understanding the properties of quadratic functions, including how to find the vertex of a parabola.
Vertex Formula – Using the vertex formula x = -b/(2a) to find the x-coordinate of the vertex.
Substitution – Substituting the x-coordinate back into the quadratic equation to find the corresponding y-coordinate.