What is the value of $$p(x)=-ig(2x+3ig)^2-4$$ when $$x=11$$ ?

To find $$p(11)$$ , substitute $$x=11$$ into the equation: $$p(11)=-ig(2(11)+3ig)^2-4$$ .

What is the axis of symmetry for the parabola represented by the equation $$p(x)=-ig(2x+3ig)^2-4$$ ?

The axis of symmetry is given by the formula $$x=-\frac{b}{2a}$$ . For the equation in standard form, it is $$x=-2$$ .

What is the x-intercept of the line represented by the equation $$y=mx+b$$ ?

The x-intercept occurs when $$y=0$$ . Solve $$0=mx+b$$ for $$x$$ .

What is the vertex of the graph represented by the equation $$p(x)=-ig(2x+3ig)^2-4$$ ?

The vertex can be found using the formula $$(-\frac{b}{2a}, p(-\frac{b}{2a}))$$ .

What is the standard form of a quadratic equation?

The standard form is $$y=ax^2+bx+c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

How do you find the vertex of a quadratic function in standard form?

The vertex can be found using the formula $$(-\frac{b}{2a}, f(-\frac{b}{2a}))$$ .

What is the significance of the leading coefficient in a quadratic function?

The leading coefficient determines the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.

What is the formula for the quadratic formula?

The quadratic formula is $$x=\frac{-b\text{±}\text{√}(b^2-4ac)}{2a}$$ .

What is the discriminant in a quadratic equation?

The discriminant is $$b^2-4ac$$ and determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

A parabola is the graph of a quadratic function, characterized by its U-shape.

What does it mean for a function to be increasing or decreasing?

A function is increasing if its output values rise as the input values increase, and decreasing if the output values fall as the input values increase.

What is a linear function?

A linear function is a polynomial function of degree 1, typically in the form $$f(x)=mx+b$$ .

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