Mathematical Methods · Unit 1 · Surds and quadratic functions · Quadratic functions
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A quadratic function is defined by \( f(x) = -2x^2 + 12x + k \), where \( k \) is a constant. The graph of \( y = f(x) \) has a zero at \( x = 7 \). (a) Determine the value of \( k \). (1 mark) (b) Determine the coordinates of the turning point of the graph of \( y = f(x) \). (2 marks) (c) Determine the other zero of the function. (1 mark)
A parabola has the equation \( y = ax^2 + bx + 18 \) and passes through the point \( (3, 0) \). The parabola has a turning point at \( x = 2 \). (a) Determine the values of \( a \) and \( b \). (3 marks) (b) Hence determine the \( y \)-coordinate of the turning point. (1 mark)
Consider the quadratic function $f(x) = 2x^2 - 8x + 3$. (a) Determine the coordinates of the turning point. [1 mark] (b) Determine the $x$-intercepts (zeros) of the function, correct to 2 decimal places. [2 marks]
Consider the quadratic function $f(x) = 2x^2 - 8x + 5$. (a) Determine the coordinates of the vertex (turning point) of the graph of $f(x)$. [1 mark] (b) Determine the zeros of $f(x)$, giving your answer in exact form. [2 marks]
For the quadratic function $f(x) = 2x^2 - 5x - 3$, determine the coordinates of the vertex (turning point).
A quadratic function is given by \( f(x) = 2x^2 + px + q \), where \( p \) and \( q \) are constants. The function has a turning point at \( (3, -7) \). (a) Determine the values of \( p \) and \( q \). (2 marks) (b) Determine the \( x \)-coordinates of the zeros of \( f(x) \), correct to two decimal places. (2 marks)
Determine the x-coordinates of the turning point and the zeros of the quadratic function f(x) = 2x² - 8x + 6.