Graph of $$f(x)=x^2$$ is reflected over x-axis and stretched horizontally to create graph of function g. Which graph could represent g?

Graph of $$g(x)=-\frac{1}{a}x^2$$ where a > 1

The graph of $$f\left(x\right)=x^2$$ was translated 4.5 units to the left to create the graph of function g. Which function represents g?

$$g\left(x\right)=\left(x+4.5\right)^2$$ .

Graph of quadratic parent function f transformed to create graph of $$g\left(x\right)=f\left(x+2\right)-5$$ . Which graph best represents g?

Graph shifted 2 units left and 5 units down.

Transformation of the graph of $$f(x)=x^2$$ to $$g(x)=(x-7.5)^2$$

A horizontal shift to the right 7.5 units

Graph transformation of $$f(x)=x^2$$ to $$h(x)=2f(x)$$ . Which graph best represents f and h?

The graph of $$h(x)=2f(x)$$ is a vertical stretch of the graph of $$f(x)=x^2$$ by a factor of 2.

The function p is in the form $$y=ax^2+c$$ . If the values of a and c are both less than 0, which graph could represent p?

A downward-opening parabola located below the x-axis.

Relationship between the graph of $$f(x)=x^2$$ and the graph of $$g(x)=7x^2$$ .

The graph of g is narrower than the graph of f.

Quadratic functions q and w are graphed on the same coordinate grid. The vertex of the graph of q is 18 units below the vertex of the graph of w. Which pair of functions could have been used to create the graphs of q and w? Options: $$q(x)=18x^2$$ and $$w(x)=x^2$$ , $$q(x)=x^2+18$$ and $$w(x)=x^2$$ , $$q(x)=-18x^2$$ and $$w(x)=x^2$$ , $$q(x)=x^2-18$$ and $$w(x)=x^2$$

$$q(x)=x^2-18$$ and $$w(x)=x^2$$

Transformations of Quadratic Functions Flashcards

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