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Find the Y-intercept of the Quadratic Function f(x)=0.3x² - 1.2x
Mathematics
Grade 9 (Junior High School)
Question Content
Find the y-intercept, the axis of symmetry, and the vertex of the graph of the function f(x)=0.3x² - 1.2x. First, answer: The y-intercept is □. (Type an ordered pair.)
Correct Answer
(0, 0)
Detailed Solution Steps
1
Step 1: Recall that the y-intercept of a function is the point where the graph crosses the y-axis, which occurs when x = 0.
2
Step 2: Substitute x = 0 into the function f(x) = 0.3x² - 1.2x: f(0) = 0.3(0)² - 1.2(0) = 0 - 0 = 0.
3
Step 3: Express the y-intercept as an ordered pair (x, y), where x=0 and y=0, so the ordered pair is (0, 0).
Knowledge Points Involved
1
Y-intercept of a quadratic function
The y-intercept of any function is the point where its graph intersects the y-axis. For any function f(x), this occurs when x=0. Substitute x=0 into the function to solve for f(0), and the y-intercept is written as the ordered pair (0, f(0)). This applies to linear, quadratic, and all polynomial functions.
2
Quadratic function form
A standard quadratic function is written in the form f(x) = ax² + bx + c, where a, b, c are constants and a ≠ 0. In this problem, a=0.3, b=-1.2, and c=0. The constant term c directly gives the y-coordinate of the y-intercept, which confirms the result here since c=0.
3
Ordered pairs for coordinate points
In the Cartesian coordinate system, points are represented as ordered pairs (x, y), where x is the horizontal coordinate (input of the function) and y is the vertical coordinate (output of the function, f(x)). This is the standard format for reporting intercepts, vertices, and all graph points.
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